1.  Corentin Briat 
 "Stability and \(L_1/l_1\)to\(L_1/l_1\) performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays" 
 (submitted) 

Abstract
BibTeX
Solutions to the interval observation problem for delayed impulsive and switched systems with \(L_1\)performance are provided. The approach is based on first obtaining stability and \(L_1/l_1\)to\(L_1/l_1\) performance analysis conditions for uncertain linear positive impulsive systems in linear fractional form with normbounded uncertainties using a scaled smallgain argument involving timevarying \(D\)scalings. Both range and minimum dwelltime conditions are formulated  the case of constant and maximum dwelltimes can be directly obtained as corollaries. The conditions are stated as timer/clockdependent conditions taking the form of infinitedimensional linear programs that can be relaxed into finitedimensional ones using polynomial optimization techniques. It is notably shown that under certain conditions, the scalings can be eliminated from the stability conditions to yield equivalent stability conditions on the socalled worstcase system, which is obtained by replacing the uncertainties by the identity matrix. These conditions are then applied to the special case of linear positive systems with delays, where the delays are considered as uncertainties, similarly to as in [C. Briat, International Journal of Control, 2017]. As before, under certain conditions, the scalings can be eliminated from the conditions to obtain conditions on the worstcase system, coinciding here with the zerodelay system  a result that is consistent with all the existing ones in the literature on linear positive systems with delays. Finally, the case of switched systems with delays is considered. The approach also encompasses standard continuoustime and discretetime systems, possibly with delays and the results are flexible enough to be extended to cope with multiple delays, timevarying delays, distributed/neutral delays and any other types of uncertain systems that can be represented as a feedback interconnection of a known system with an uncertainty.
@article{Briat:18J,
author = "C. Briat",
title = "Stability and /ll_1$to/ll_1$ performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays",
journal = "(submitted)",
volume = "",
pages = "",
year = "2018",
}



2.  Corentin Briat and Mustafa Khammash 
 "Robust and Structural Ergodicity Analysis and Antithetic Integral Control of Stochastic Reaction Networks" 
 (submitted) 

Abstract
BibTeX
Various regulation motifs have been discovered or posited over the recent years, the most recent one being the socalled Antithetic Integral Control (AIC) motif [Briat, Gupta & Khammash, Cell Systems, 2017]. Several favorable properties for the AIC motif have been demonstrated for classes of reaction networks that satisfy certain irreducibility, ergodicity and output controllability conditions. Here we address the problem of verifying these conditions for large sets of reaction networks with fixed topology using three different approaches. The first one is quantitative and relies on the notion of interval matrices, the second one is qualitative and is based on sign properties of matrices and the last one is a direct approach where the parameter dependence is exactly taken into account. The obtained results lie in the same spirit as those obtained in [Briat, Gupta & Khammash, Cell Systems, 2017] where properties of reaction networks are independently characterized in terms of control theoretic concepts, linear programs, and graph theoretic and algebraic conditions.
@article{Briat:18I,
author = "C. Briat and M. Khammash",
title = "Robust and Structural Ergodicity Analysis and Antithetic Integral Control of Stochastic Reaction Networks",
journal = "(submitted)",
volume = "",
pages = "",
year = "2018",
}



3.  Corentin Briat and Mustafa Khammash 
 "InSilico ProportionalIntegral Moment Control of Stochastic Reaction Networks with Applications to Gene Expression (with Dimerization)" 
 (submitted) 

Abstract
BibTeX
The problem of controlling the mean and the variance of a species of interest in a simple gene expression is addressed. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a simple PI controller that satisfies certain sufficient conditions. Controlling both the mean and variance however requires an additional control input, e.g. the mRNA degradation rate, and local robust tracking of mean and variance is proved to be achievable using multivariable PI control, provided that the reference point satisfies necessary conditions imposed by the system. Even more importantly, it is shown that there exist PI controllers that locally, robustly and simultaneously stabilize all the equilibrium points inside the admissible region. The results are then extended to the mean control of a gene expression with protein dimerization. It is shown that the moment closure problem can be circumvented without invoking any moment closure technique. Local stabilization and convergence of the average dimer population to any desired reference value is ensured using a pure integral control law. Explicit bounds on the controller gain are provided and shown to be valid for any reference value. As a byproduct, an explicit upperbound of the variance of the monomer species, acting on the system as unknown input due to the moment openness, is obtained. The results are illustrated by simulation.
@article{Briat:18H,
author = "C. Briat and M. Khammash",
title = "InSilico ProportionalIntegral Moment Control of Stochastic Reaction Networks with Applications to Gene Expression (with Dimerization)",
journal = "(submitted)",
volume = "",
pages = "",
year = "2018",
}



4.  Corentin Briat 
 "A class of \(L_1\)to\(L_1\) and \(L_\infty\)to\(L_\infty\) interval observers for (delayed) Markov jump linear systems" 
 (submitted) 

Abstract
BibTeX
We exploit recent results on the stability and performance analysis of positive Markov jump linear systems (MJLS) for the design of interval observers for MJLS with and without delays. While the conditions for the \(L_1\) performance are necessary and sufficient, those for the \(L_\infty\) performance are only sufficient. All the conditions are stated as linear programs that can be solved very efficiently. Two examples are given for illustration.
@article{Briat:18D,
author = "C. Briat",
title = "A class of $to$ and \infty$to\infty$ interval observers for (delayed) Markov jump linear systems",
journal = "(submitted)",
volume = "",
pages = "",
year = "2018",
}



5.  Corentin Briat 
 "\(L_1/l_1\)to\(L_1/l_1\) analysis of linear positive impulsive systems with application to the \(L_1/l_1\)to\(L_1/l_1\) interval observation of linear impulsive and switched systems" 
 (submitted) 

Abstract
BibTeX
Sufficient conditions characterizing the asymptotic stability and the hybrid /l_1$gain of linear positive impulsive systems underinimum and range dwelltime constraints are obtained. These conditions are stated as infinitedimensional linear programming problems that can be solved using sum of squares programming, a relaxation that is known to be asymptotically exact in the present case. These conditions are then adapted to formulate constructive and convex sufficient conditions for the existence of \(L_1/l_1\)to\(L_1/l_1\) interval observers for linear impulsive and switched systems. Suitable observer gains can be extracted from the (suboptimal) solution of the infinitedimensional optimization problem where the \(L_1/l_1\)gain of the system mapping the disturbances to the weighted observation errors is minimized. Some examples on impulsive and switched systems are given for illustration.
@article{Briat:18C,
author = "C. Briat",
title = "/ll_1$to/ll_1$ analysis of linear positive impulsive systems with application to the /ll_1$to/ll_1$ interval observation of linear impulsive and switched systems",
journal = "(submitted)",
volume = "",
pages = "",
year = "2018",
}



6.  Corentin Briat 
 "Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampleddata controllers" 
 (submitted) 

Abstract
BibTeX
Linear ParameterVarying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far. We fill this gap here by proposing an approach relying on the reformulation of the considered LPV system as an extended equivalent hybrid system that will incorporate, through a suitable state augmentation, information on both the dynamics of the state of the system and the considered class of parameter trajectories. Two stability conditions are established using a result pertaining on the stability of hybrid systems and shown to naturally generalize and unify the wellknown quadratic and robust stability criteria together. The obtained conditions being infinitedimensional semidefinite programming problems, a relaxation approach based on sum of squares programming is used in order to obtain tractable finitedimensional conditions. The conditions are then losslessly extended to solve two control problems, namely, the stabilization by continuous and sampleddata gainscheduled statefeedback controllers. The approach is finally illustrated on several examples from the literature.
@article{Briat:18B,
author = "C. Briat",
title = "Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampleddata controllers",
journal = "(submitted)",
volume = "",
pages = "",
year = "2018",
}



7.  Corentin Briat 
 "Codesign of aperiodic sampleddata minjumping rules for linear impulsive, switched impulsive and sampleddata systems" 
 (submitted) 

Abstract
BibTeX
An aperiodic sampleddata minjumping rule is proposed for linear impulsive systems, a class of systems encompassing switched and sampleddata systems as particular cases. Several sufficient codesign conditions characterizing the stabilization of a given linear impulsive system subject to the considered minjumping rule and a sampleddata statefeedback controller are formulated in terms of discretetime LyapunovMetzler conditions. These conditions are then exactly reformulated as clockdependent conditions known to be more convenient to verify and that allow for an immediate extension of the results to uncertain systems and to performance analysis. Several examples pertaining on sampleddata control of switched and impulsive systems are given for illustration.
@article{Briat:18A,
author = "C. Briat",
title = "Codesign of aperiodic sampleddata minjumping rules for linear impulsive, switched impulsive and sampleddata systems",
journal = "(submitted)",
volume = "",
pages = "",
year = "2018",
}



8.  Corentin Briat, Ankit Gupta and Mustafa Khammash 
 "Antithetic proportionalintegral feedback for reduced variance and improved control performance of stochastic reaction networks" 
 Accepted in the Journal of the Royal Society: Interface 

Abstract
BibTeX
The antithetic integral feedback motif recently introduced in Briat, Gupta & Khammash (Cell Systems, 2017) is known to ensure robust perfect adaptation for the mean dynamics of a given molecular species involved in a complex stochastic biomolecular reaction network. However, it was observed that it also leads to a higher variance in the controlled network than that obtained when using a constitutive (i.e. openloop) control strategy. This was interpreted as the cost of the adaptation property and may be viewed as a performance deterioration for the overall controlled network. To decrease this variance and improve the performance, we propose to combine the antithetic integral feedback motif with a negative feedback strategy. Both theoretical and numerical results are obtained. The theoretical ones are based on a tailored moment closure method allowing one to obtain approximate expressions for the stationary variance for the controlled network and predict that the variance can indeed be decreased by increasing the strength of the negative feedback. Numerical results verify the accuracy of this approximation and show that the controlled species variance can indeed be decreased, sometimes below its constitutive level. Three molecular networks are considered in order to verify the wide applicability of two types of negative feedback strategies. The main conclusion is that there is a tradeoff between the speed of the settlingtime of the mean trajectories and the stationary variance of the controlled species; i.e. smaller variance is associated with larger settlingtime.
@article{Briat:18G,
author = "C. Briat and A. Gupta and M. Khammash",
title = "Antithetic proportionalintegral feedback for reduced variance and improved control performance of stochastic reaction networks",
journal = "Accepted in the Journal of the Royal Society: Interface",
volume = "",
pages = "",
year = "2018",
}



9.  Corentin Briat 
 "Stability analysis and statefeedback control of LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps" 
 IEEE Control Systems Letters, Vol. 2(2), pp. 230235, 2018 

Abstract
BibTeX
LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps are a class of systems that does not seem to have been thoroughly considered in the literature. We partially fill this gaphere by providing sufficient stability and performance analysis conditions stated in terms of infinitedimensional LMI problems that can be solved using sum of squares programming. A particularity of the obtained conditions lies in the presence of an integral term leading to some technical difficulties when attempting to obtain convex conditions for the design of a gainscheduled statefeedback controller. This difficulty is circumvented by relying on a recent result for timedelay systems analysis and an equivalent integralfree LMI condition is obtained. The approach is illustrated through several examples.
@article{Briat:18E,
author = "C. Briat",
title = "Stability analysis and statefeedback control of LPV systems with piecewise constant parameters subject to spontaneous Poissonian jumps",
journal = "IEEE Control Systems Letters",
volume = "2(2)",
pages = "230235",
year = "2018",
}



10.  Corentin Briat and Mustafa Khammash 
 "Dynamic integral control ensures robust perfect adaptation and optimal equilibrium productivity for a microbial biofuel metabolic pathway" 
 ACS Synthetic Biology, Vol. 7(2), pp. 419431, 2018 

Abstract
BibTeX
The production of complex biomolecules by genetically engineered organisms is one of the most promising applications of metabolic engineering and synthetic biology. To obtain processes with high productivity, it is therefore crucial to design and implement efficient dynamic invivo regulation strategies. We consider here the microbial biofuel production model of Dunlop et al. (2010) for which we demonstrate that an antithetic dynamic integral control strategy can achieve robust perfect adaptation for the intracellular biofuel concentration in presence of poorly known network parameters and implementation errors in certain rate parameters of the controller. We also show that the maximum equilibrium extracellular biofuel productivity is fully defined by some of the network parameters and, in this respect, it can only be achieved when all the corresponding parameters are perfectly known. Since this optimum is a network property, it cannot be improved by the use of any controller that measures the intracellular biofuel concentration and acts on the production of pump proteins. Additional intrinsic fundamental properties for the process are also unveiled, the most important ones being the existence of a conservation relation between the productivity and the toxicity, a low sensitivity of the optimal productivity with respect to a poor implementation of the setpoint for the intracellular biofuel, and a strong intrinsic robustness property of the optimal productivity with respect to poorly known parameters. Taken together, these results demonstrate that a high and robust equilibrium rate of production for the extracellular biofuel can be achieved when the parameters of the model are poorly known and those of the controllers are poorly implemented. Finally, several advantages of the proposed dynamic strategy over a static one are also emphasized.
@article{Briat:18F,
author = "C. Briat and M. Khammash",
title = "Dynamic integral control ensures robust perfect adaptation and optimal equilibrium productivity for a microbial biofuel metabolic pathway",
journal = "ACS Synthetic Biology",
volume = "7(2)",
pages = "419431",
year = "2018",
}



11.  Corentin Briat 
 "Stability and performance analysis of linear positive systems with delays using inputoutput methods" 
 International Journal of Control (in press) 

Abstract
BibTeX
It is known that inputoutput approaches based on scaled smallgain theorems with constant \(D\)scalings and integral linear constraints are nonconservative for the analysis of some classes of linear positive systems interconnected with uncertain linear operators. This dramatically contrasts with the case of general linear systems with delays where inputoutput approaches provide, in general, sufficient conditions only. Using these results we provide simple alternative proofs for many of the existing results on the stability of linear positive systems with discrete/distributed/neutral timeinvariant/varying delays and linear difference equations. In particular, we give a simple proof for the characterization of diagonal Riccati stability for systems with discretedelays and generalize this equation to other types of delay systems. The fact that all those results can be reproved in a very simple way demonstrates the importance and the efficiency of the inputoutput framework for the analysis of linear positive systems. The approach is also used to derive performance results evaluated in terms of the \(L_1\), \(L_2\) and \(L_\infty\)gains. It is also flexible enough to be used for design purposes.
@article{Briat:17ijc,
author = "C. Briat",
title = "Stability and performance analysis of linear positive systems with delays using inputoutput methods",
journal = "International Journal of Control (in press)",
volume = "",
pages = "",
year = "2017",
}



12.  Corentin Briat 
 "Dwelltime stability and stabilization conditions for linear positive impulsive and switched systems" 
 Nonlinear Analysis: Hybrid Systems, Vol. 24, pp. 198226, 2017. 

Abstract
BibTeX
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwelltime are obtained. The proposed stability conditions characterize the pointwise decrease of a linear copositive Lyapunov function and are formulated in terms of finitedimensional or semiinfinite linear programs. To be applicable to uncertain systems and to control design, a lifting approach is then considered in order to make the conditions affine in the matrices of the system. The resulting stability and stabilization conditions are stated as infinitedimensional linear programs for which three asymptotically exact approximate computational methods are proposed and compared with each other on numerical examples. Similar results are then obtained for linear positive switched systems by exploiting the possibility of reformulating a switched system as an impulsive system. Some existing stability conditions are retrieved and extended to stabilization using the proposed lifting approach. Several examples are finally given for illustration.
@article{Briat:17b,
author = "C. Briat",
title = "Dwelltime stability and stabilization conditions for linear positive impulsive and switched systems",
journal = "Nonlinear Analysis: Hybrid Systems",
volume = "24",
pages = "198226",
year = "2017",
}



13.  Corentin Briat 
 "Sign properties of Metzler matrices with applications" 
 Linear Algebra and Its Applications, Vol. 515, pp. 5386, 2017. 

Abstract
BibTeX
Several results about sign properties of Metzler matrices are obtained. It is first established that checking the signstability of a Metzler signmatrix can be either characterized in terms of the Hurwitz stability of the unit signmatrix in the corresponding qualitative class, or in terms the negativity of the diagonal elements of the Metzler signmatrix and the acyclicity of the associated directed graph. Similar results are obtained for the case of Metzler blockmatrices and Metzler mixedmatrices, the latter being a class of Metzler matrices containing both sign and realtype entries. The problem of assessing the signstability of the convex hull of a finite and summable family of Metzler matrices is also solved, and a necessary and sufficient condition for the existence of common Lyapunov functions for all the matrices in the convex hull is obtained. The concept of signstability is then generalized to the concept of Ker_+(B)\)signstability, a problem that arises in the analysis of certain jump Markov processes. A sufficient condition for the Ker\(_+(B)\)signstability of Metzler signmatrices is obtained and formulated using inverses of signmatrices and the concept of \(L^+\)matrices. Several applications of the results are discussed in the last section.
@article{Briat:17a,
author = "C. Briat",
title = "Sign properties of Metzler matrices with applications",
journal = "Linear Algebra and Its Applications",
volume = "515",
pages = "5386",
year = "2017",
}



14.  Corentin Briat 
 "Stability analysis and stabilization of stochastic linear impulsive, switched and sampleddata systems under dwelltime constraints" 
 Automatica, Vol. 74, pp. 279287, 2016 

Abstract
BibTeX
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampleddata systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting. The concepts of meansquare stability and dwelltimes are utilized in order to formulate relevant stability conditions for such systems. These conditions are formulated as convex clockdependent linear matrix inequality conditions that are applicable to robust analysis and control design, and are verifiable using discretization or sum of squares techniques. Stability conditions under various dwelltime conditions are obtained and nonconservatively turned into statefeedback stabilization conditions. The results are finally applied to the analysis and control of stochastic sampleddata systems. Several comparative examples demonstrate the accuracy and the tractability of the approach.
@article{Briat:16c,
author = "C. Briat",
title = "Stability analysis and stabilization of stochastic linear impulsive, switched and sampleddata systems under dwelltime constraints",
journal = "Automatica",
volume = "74",
pages = "279287",
year = "2016",
}



15.  Corentin Briat and Mustafa Khammash 
 "Interval peaktopeak observers for continuous and discretetime systems with persistent inputs and delays" 
 Automatica, Vol. 74, pp. 206213, 2016 

Abstract
BibTeX
While the design of optimal peaktopeak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the error dynamics. By indeed exploiting several recent results on positive systems, we propose a novel and nonconservative approach formulated in terms of a tractable finitedimensional linear program for designing a class of interval observers achieving minimum peaktopeak gain. The optimal observer is notably shown to be uniform over the set of all possible maps between observation errors and their weighted versions, which parallels a recent result pertaining on the stabilization of linear positive system. Results pertaining on the interval observation of timedelay and discretetime systems are then obtained as a direct application of the proposed method, emphasizing then its flexibility. Several examples pertaining on the observation of linear and nonlinear systems are finally given for illustration.
@article{Briat:16b,
author = "C. Briat and M. Khammash",
title = "Interval peaktopeak observers for continuous/discretetime systems with persistent inputs and delays",
journal = "Automatica",
volume = "74",
pages = "206213",
year = "2016",
}



16.  Corentin Briat, Christoph Zechner and Mustafa Khammash 
 "Design of a synthetic integral feedback circuit: dynamic analysis and DNA implementation" 
 SNSF News article by Atlant Bieri ACS Synthetic Biology, Vol. 5(10), pp. 11081116, 2016 

Abstract
BibTeX
The design and implementation of regulation motifs ensuring robust perfect adaptation are challenging problems in synthetic biology. Indeed, the design of highyield robust metabolic pathways producing, for instance, drug precursors and biofuels, could be easily imagined to rely on such a control strategy in order to optimize production levels and reduce production costs, despite the presence of environmental disturbance and model uncertainty. We propose here a motif that ensures tracking and robust perfect adaptation for the controlled reaction network through integral feedback. Its metabolic load on the host is fully tunable and can be made arbitrarily close to the constitutive limit, the universal minimal metabolic load of all possible controllers. A DNA implementation of the controller network is finally provided. Computer simulations using realistic parameters demonstrate the good agreement between the DNA implementation and the ideal controller dynamics.
@article{Briat:16,
author = "C. Briat and C. Zechner and M. Khammash",
title = "Design of a synthetic integral feedback circuit: dynamic analysis and DNA implementation",
journal = "ACS Synthetic Biology",
volume = "5(10)",
pages = "11081116",
year = "2016",
}



17.  Corentin Briat 
 "Theoretical and numerical comparisons of looped functionals and clockdependent Lyapunov functions—The case of periodic and pseudoperiodic systems with impulses" 
 International Journal of Robust and Nonlinear Control, Vol. 26(10), pp. 22322255, 2016 

Abstract
BibTeX
The stability of uncertain periodic and pseudoperiodic systems with impulses is analyzed in the loopedfunctional and clockdependent Lyapunov function frameworks. These alternative and equivalent ways for characterizing discretetime stability have the benefit of leading to stability conditions that are convex in the system matrices, hence suitable for robust stability analysis. These approaches, therefore, circumvent the problem of computing the monodromy matrix associated with the system, which is known to be a major difficulty when the system is uncertain. Convex stabilization conditions using a nonrestrictive class of statefeedback controllers are also provided. The obtained results readily extend to uncertain impulsive periodic and pseudoperiodic systems, a generalization of periodic systems that admit changes in the ‘period’ from one pseudoperiod to another. The obtained conditions are expressed as infinitedimensional semidefinite programs, which can be solved using recent polynomial programming techniques. Several examples illustrate the approach, and comparative discussions between the different approaches are provided. A major result obtained in the paper is that despite being equivalent, the approach based on looped functional reduces to the one based on clockdependent Lyapunov functions when a particular structure for the looped functional is considered. The conclusion is that the approach based on clockdependent Lyapunov functions is preferable because of its lower computational complexity and its convenient structure enabling control design.
@article{Briat:16IJRNC,
author = "C. Briat",
title = "Theoretical and numerical comparisons of looped functionals and clockdependent Lyapunov functions—The case of periodic and pseudoperiodic systems with impulses",
journal = "International Journal of Robust and Nonlinear Control",
volume = "26(10)",
pages = "22322255",
year = "2016",
}



18.  Corentin Briat, Ankit Gupta and Mustafa Khammash 
 "Antithetic Integral Feedback ensures robust perfect adaptation in noisy bimolecular networks (Featured Article)" 
 Preview Article by John Doyle, Commentary Article by James Ferrell, ETH News article by Peter Rüegg, SNSF News article by Atlant Bieri
Cell Systems, Vol. 2(1), pp. 1728, 2016 

Abstract
BibTeX
The ability to adapt to stimuli is a defining feature of many biological systems and critical to maintaining homeostasis. While it is well appreciated that negative feedback can be used to achieve homeostasis when networks behave deterministically, the effect of noise on their regulatory function is not understood. Here, we combine probability and control theory to develop a theory of biological regulation that explicitly takes into account the noisy nature of biochemical reactions. We introduce tools for the analysis and design of robust homeostatic circuits and propose a new regulation motif, which we call antithetic integral feedback. This motif exploits stochastic noise, allowing it to achieve precise regulation in scenarios where similar deterministic regulation fails. Specifically, antithetic integral feedback preserves the stability of the overall network, steers the population of any regulated species to a desired set point, and adapts perfectly. We suggest that this motif may be prevalent in endogenous biological circuits and useful when creating synthetic circuits.
@article{Briat:16a,
author = "C. Briat and A. Gupta and M. Khammash",
title = "Antithetic Integral Feedback ensures robust perfect adaptation in noisy bimolecular networks",
journal = "Cell Systems",
volume = "2(1)",
pages = "1728",
year = "2016",
}



19.  Weiming Xiang, Guisheng Zhai and Corentin Briat 
 "Stability analysis for LTI control systems with controller failures and its application in failure tolerant control" 
 IEEE Transactions on Automatic Control, Vol. 61(3), pp. 811816, 2016 

Abstract
BibTeX
In this technical note, the stability and failure tolerant control are investigated for linear timeinvariant (LTI) control systems with occasional controller failures. At first, a collection of nonconvex sufficient conditions ensuring the closed loop to be globally asymptotically stable is presented, which are simple to use but difficult to consider for control purpose. To overcome this, a timescheduled Lyapunov function approach is considered and alternative convex conditions are obtained. Based on this result, a timedependent failuretolerant controller is designed. The approach is finally illustrated on a networked control system.
@article{TAC:16,
author = "C. Briat",
title = "Stability analysis for {LTI} control systems with controller failures and its application in failure tolerant control",
journal = "IEEE Transactions on Automatic Control",
volume = "61(3)",
pages = "811816",
year = "2016",
}



20.  Corentin Briat 
 "Stability analysis and control of a class of LPV systems with piecewise constant parameters" 
 Systems & Control Letters, Vol. 82, pp. 1017, 2015 

Abstract
BibTeX
Stability criteria characterizing the asymptotic stability of a class of LPV systems with piecewise constant parameters under constant and minimum dwelltime are derived. It is shown that, for such systems, the conditions for the stability under minimum dwelltime can be seen as a unifying stability concept lying in between quadratic and robust stability, thereby including them as extremal cases. The results are then extended to address the stabilization problem using a particular class of timedependent gainscheduled statefeedback controllers. Several examples are given for illustration.
@article{Briat:15d,
author = "C. Briat",
title = "Stability analysis and control of a class of {LPV} systems with piecewise constant parameters",
journal = "Systems \& Control Letters",
volume = "82",
pages = "1017",
year = "2015",
}



21.  Corentin Briat and Alexandre Seuret 
 "On the necessity of loopedfunctionals arising in the analysis of pseudoperiodic, sampleddata and hybrid systems" 
 International Journal of Control, Vol. 88(12), pp. 25632569, 2015 

Abstract
BibTeX
Loopedfunctionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous papers on the analysis of sampleddata, impulsive and switched systems have only been shown to be sufficient for the characterisation of their associated discretetime stability conditions. We prove here that these conditions are also necessary. This result is derived for a wider class of linear systems, referred to as impulsive pseudoperiodic systems, that encompass periodic, impulsive, sampleddata and switched systems as special cases.
@article{Briat:15IJC,
author = "C. Briat and A. Seuret",
title = "On the necessity of loopedfunctionals arising in the analysis of pseudoperiodic, sampleddata and hybrid systems",
journal = "Systems \& Control Letters",
volume = "88(12)",
pages = "25632569",
year = "2015",
}



22.  Corentin Briat 
 "Convex conditions for the robust stabilization of uncertain switched systems with guaranteed minimum and modedependent dwelltime" 
 Systems & Control Letters, Vol. 78, pp. 6372, 2015 

Abstract
BibTeX
Alternative conditions for establishing dwelltime stability properties of linear switched systems are considered. Unlike the hybrid conditions derived in Geromel and Colaneri (2006), the considered ones are affine in the system matrices, allowing then for the consideration of uncertain switched systems with timevarying uncertainties. The low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of statefeedback control laws. The resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or loopedfunctionals previously considered in the literature. The sums of squares conditions are also proven to (1) approximate arbitrarily well the conditions of Geromel and Colaneri (2006); and (2) be invariant with respect to timescaling, emphasizing that the complexity of the approach does not depend on the size of the dwelltime. Several comparative examples illustrate the efficiency of the approach.
@article{Briat:15c,
author = "C. Briat",
title = "Convex conditions for the robust stabilization of uncertain switched systems with guaranteed minimum and modedependent dwelltime",
journal = "Systems \& Control Letters",
volume = "78",
pages = "6372",
year = "2015",
}



23.  Alexandre Seuret and Corentin Briat 
 "Stability analysis of uncertain sampleddata systems with incremental delay using loopedfunctionals" 
 Automatica, Vol. 55, pp. 274278, 2015. 

Abstract
BibTeX
The robust stability analysis of asynchronous and uncertain sampleddata systems with constant incremental input delay is addressed in the loopedfunctional framework. These functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discretetime stability conditions in an affine way, enabling then the consideration of uncertain and timevarying systems. The stability conditions are obtained by first reformulating the sampleddata system as an impulsive system, and by then considering a tailored loopedfunctional along with Wirtinger’s inequality, a recently introduced inequality that has been shown to be less conservative than Jensen’s inequality. Several examples are given for illustration.
@article{SeuretBriat:15a,
author = "A. Seuret and C. Briat",
title = "Stability analysis of uncertain sampleddata systems with incremental delay using loopedfunctionals",
journal = "Automatica",
volume = "55",
pages = "274278",
year = "2015",
}



24.  Corentin Briat, Emre Altug Yavuz, Håkan Hjalmarsson, Karl Henrik Johansson, Ulf T. Jönsson, Gunnar Karlsson and Henrik Sandberg 
 "The conservation of information, towards an axiomatized modular modeling approach to congestion control" 
 IEEE Transactions on Networking, Vol. 23(3), pp. 851865, 2015 

Abstract
BibTeX
We derive a modular fluidflow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance indicators like sending/acknowledgment rates and delays are mathematically modeled by applying this law locally. Our contributions are twofold. First, we introduce a modular metamodel that is sufficiently generic to represent any network topology. The proposed model is composed of building blocks that implement mechanisms ignored by the existing ones, which can be recovered from exact reduction or approximation of this new model. Second, we provide a novel classification of previously proposed models in the literature and show that they are often not capable of capturing the transient behavior of the network precisely. Numerical results obtained from packetlevel simulations demonstrate the accuracy of the proposed model.
@article{Briat:15ToN,
author = "C. Briat and E. A. Yavuz and H. Hjalmarsson and K.H. Johansson and U. T. J{"{o}}nsson and G. Karlsson and H. Sandberg",
title = "The conservation of information, towards an axiomatized modular modeling approach to congestion control",
journal = "To appear in the {IEEE} Transactions on Networking",
volume = "23(3)",
pages = "851865",
year = "2015",
}



25.  Ankit Gupta, Corentin Briat and Mustafa Khammash 
 "A scalable computational framework for establishing longterm behavior of stochastic reaction networks" 
 PLOS Computational Biology, Vol. 10(6), e1003669, 2014 

Abstract
BibTeX
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now wellestablished that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the longterm behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, wellknown for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a nonergodic biological network are also discussed.
@article{Briat:14PLOS,
author = "A. Gupta and C. Briat and M. Khammash",
title = "A scalable computational framework for establishing longterm behavior of stochastic reaction networks",
journal = "PLOS Computational Biology",
year = "2014",
volume = "10(6)",
pages="e1003669",
url="http://arxiv.org/abs/1304.5404",
}



26.  Corentin Briat 
 "Convex lifted conditions for robust \(l_2\)stability analysis and \(l_2\)stabilization of linear discretetime switched systems with minimum dwelltime constraint" 
 Automatica, Vol. 50(3), pp. 976983, 2014 

Abstract
BibTeX
Stability analysis of discretetime switched systems under minimum dwelltime is studied using a new type of LMI conditions. These conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in Geromel and Colaneri (2006b). The convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables. The convexity of the conditions can be exploited to extend the results to uncertain systems, control design and l2gain computation without introducing additional conservatism. Several examples are presented to show the effectiveness of the approach.
@article{Briat:14auto,
author = "C. Briat",
title = "Convex lifted conditions for robust $ll_2$stability analysis and $ll_2$stabilization of linear discretetime switched systems with minimum dwelltime constraint",
journal = "Automatica",
volume = "50(3)",
pages = "976983",
year = "2014",
}



27.  Corentin Briat 
 "Spectral necessary and sufficient conditions for samplingperiodindependent stabilization of periodic and aperiodic sampleddata systems using a class of generalized sampleddata hold functions" 
 International Journal of Control, Vol. 87(3), pp. 612621, 2014 

Abstract
BibTeX
Samplingperiodindependent (SPI) stabilization of both periodic and aperiodic sampleddata systems using a class of generalized sampleddata hold functions is addressed. It is proved that for this specific class of hold functions, a continuoustime linear system with rankminimal input matrix and with nondefective eigenvalues on the imaginary axis is SPIstabilizable if and only if the spectrum of the system is contained in the closed lefthalf plane. A systematic procedure for constructing suitable statefeedback controllers is also provided. Several examples are finally discussed for illustration.
@article{Briat:14ijc,
author = "C. Briat",
title = "Spectral necessary and sufficient conditions for samplingperiodindependent stabilization of periodic and aperiodic sampleddata systems using a class of generalized sampleddata hold functions",
journal = "International Journal of Control",
volume = "87",
issue = "3",
pages = "612621",
year = "2014",
}



28.  Corentin Briat 
 "Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampleddata systems under dwelltime constraints" 
 Automatica, Vol. 49(11), pp. 33493457, 2013 

Abstract
BibTeX
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuoustime timevarying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to stability of aperiodic systems under minimum, maximum and ranged dwelltimes are then derived. By exploiting further the particular structure of the stability conditions, the results are nonconservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of statefeedback controllers, providing then a convex solution to the open problem of robust dwelltime stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampleddata systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampleddata systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.
@article{Briat:13auto,
author = "C. Briat",
title = "Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampleddata systems under dwelltime constraints",
journal = "Automatica",
volume = "49(11)",
pages = "34493457",
year = "2013",
}



29.  Burak Demirel, Corentin Briat and Mikael Johansson 
 "Deterministic and Stochastic Approaches to Supervisory Control Design for Networked Systems with TimeVarying Communication Delays" 
 Nonlinear Analysis: Hybrid Systems, Vol. 10, pp. 94110, 2013 

Abstract
BibTeX
This paper proposes a supervisory control structure for networked systems with timevarying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multicontroller unit, aims at improving the closedloop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwelltime switching and is based on a novel multiple LyapunovKrasovskii functional. We develop stability conditions that can be verified by semidefinite programming, and show that the associated state feedback synthesis problem also can be solved using convex optimization tools. Extensions of the analysis and synthesis procedures to the case when the evolution of the delay mode is described by a Markov chain are also developed. Simulations on small and largescale networked control systems are used to illustrate the effectiveness of our approach.
@article{Demirel:13nshs,
author = "B. Demirel and C. Briat and M. Johansson",
title = "Deterministic and Stochastic Approaches to Supervisory Control Design for Networked Systems with TimeVarying Communication Delays",
journal = "Nonlinear Analysis: Hybrid Systems",
year = "2013",
volume = "10",
pages ="94110",
}



30.  Corentin Briat 
 "Robust stability and stabilization of uncertain linear positive systems via Integral Linear Constraints: \(L_1\) and \(L_\infty\)gains characterization" 
 International Journal of Robust and Nonlinear Control, Vol. 23(17), pp. 19321954, 2013. 

Abstract
BibTeX
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supplyrates are employed here for robustness and performance analysis using \(L_1\) and \(L_\infty\)gains. Robust stability analysis is performed using Integral Linear Constraints (ILCs) for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's Theorem. Several examples are provided for illustration.
@article{Briat:ijrnc13,
author = "C.~Briat",
title = "Robust stability and stabilization of uncertain linear positive systems via Integral Linear Constraints: _1$ and _\infty$gains characterization",
year = "2013",
journal = "International Journal of Robust and Nonlinear Control"
volume ="23(17)",
pages ="19321954",
}



31.  Corentin Briat and Alexandre Seuret 
 "Affine characterizations of minimal and modedependent dwelltimes for uncertain linear switched systems" 
 IEEE Transactions on Automatic Control, Vol. 58(5), pp. 13041310, 2013. 

Abstract
BibTeX
An alternative approach for minimum and modedependent dwelltime characterization for switched systems is derived. The proposed technique is related to Lyapunov loopedfunctionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwelltime. These conditions are expressed as infinitedimensional LMIs which can be solved using recent polynomial optimization techniques such as sumofsquares. The specific structure of the conditions is finally utilized in order to derive dwelltime stability results for uncertain switched systems. Several examples illustrate the efficiency of the approach.
@article{Briat:13tac2,
author = "C. Briat and A. Seuret",
title = "Affine characterizations of minimal and modedependent dwelltimes for uncertain linear switched systems",
journal = "{IEEE} Transactions on Automatic Control",
year = "2013",
volume ="58(5)",
pages ="13041310",
}



32.  Corentin Briat and Olivier Sename 
 "Discussion on "Timedelay modelbased control of the glucoseinsulin system, by means of a state observer"" 
 European Journal of Control, Vol. 18(6), pp. 607609, 2012 




33.  Corentin Briat and Alexandre Seuret 
 "Convex dwelltime characterizations for uncertain linear impulsive systems" 
 IEEE Transactions on Automatic Control, Vol. 57(12), pp. 32413246, 2012 

Abstract
BibTeX
New sufficient conditions for the characterization of dwelltimes for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of loopedfunctionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve nonmonotonically along the flow of the system in a new way, broadening then the admissible class of systems which may be analyzed. As a byproduct, the particular structure of the obtained conditions makes the method is easily extendable to uncertain systems by exploiting some convexity properties. Several examples illustrate the approach.
@article{Briat:13tac,
author = "C. Briat and A. Seuret",
title = "Convex dwelltime characterizations for uncertain linear impulsive systems",
journal = "{IEEE} Transactions on Automatic Control",
volume ="57(12)",
pages ="32413246",
year = "2012",
}



34.  Corentin Briat and Alexandre Seuret 
 "A loopedfunctional approach for robust stability analysis of linear impulsive systems" 
 Systems & Control Letters, Vol. 61, pp. 980988, 2012 

Abstract
BibTeX
A new functionalbased approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces loopedfunctionals, considers nonmonotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwelltimes results, for both certain and uncertain systems. It is also shown that this approach may be applied to a wider class of impulsive systems than existing methods. Some examples, notably on sampleddata systems, illustrate the efficiency of the approach.
@article{Briat:12scl,
author = "C. Briat and A. Seuret",
title = "A loopedfunctional approach for robust stability analysis of linear impulsive systems",
journal = "Systems & Control Letters",
pages ="980988",
volume ="61",
year = "2012",
}



35.  Corentin Briat, Olivier Sename and JeanFrançois Lafay 
 "Design of LPV observers for LPV TimeDelay Systems: An Algebraic Approach" 
 International Journal of Control, Vol. 84(9), pp. 15331542, 2012 

Abstract
BibTeX
The design of reducedorder observer for LPV timedelay systems is addressed. Necessary conditions
guaranteeing primordial structural properties for the observation error dynamics are first provided through nonlinear
algebraic matrix equalities. Then, an explicit parameterization of the family of observers fulfilling these necessary
conditions is derived. Finally, two slightly different LMIbased approaches are provided to select an
observer within this family according to some criterion; e.g. maximization of the delaymargin or guaranteed
suboptimal \(\mathcal{L}_2\)gain. An example from the literature is used to illustrate the efficiency of the approach.
@article{Briat:ijc11,
author = "C.~Briat and O.~Sename and JF.~Lafay",
title = "Design of LPV observers for LPV TimeDelay Systems: An Algebraic Approach",
year = "2011",
journal = "International Journal of Control"
volume ="84(9)",
pages ="15331542",
url="http://dx.doi.org/10.1080/00207179.2011.611950",
}



36.  Corentin Briat 
 "Convergence and Equivalence results for the Jensen's inequality  Application to timedelay and sampleddata systems" 
 IEEE Transactions on Automatic Control, Vol. 56(7), pp. 16601665, 2011 

Abstract
BibTeX
The Jensen's inequality plays a crucial role in the analysis of timedelay and sampleddata systems. Its conservatism is studied through the use of the Gr"{u}ss Inequality. It has been reported in the literature that fragmentation (or partitioning) schemes allow to empirically improve the results. We prove here that the Jensen's gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large. Nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases. Finally, a family of bounds is characterized and a comparison with other bounds of the literature is provided. It is shown that the other bounds are equivalent to Jensen's and that they exhibit interesting wellposedness and linearity properties which can be exploited to obtain better numerical results.
@article{Briat:tac11,
author = "C.~Briat",
title = "Convergence and Equivalence results for the Jensen's inequality  Application to timedelay and sampleddata systems",
year = "2011",
journal = "IEEE Transactions on Automatic Control",
url = "http://dx.doi.org/10.1109/TAC.2011.2121410",
pages = "16601665",
volume = "56(7)",
}



37.  Emmanuel Witrant, Pergiuseppe di Marco, Pangun Park and Corentin Briat 
 "Limitations and Performances of Robust Control over WSN: UFAD Control in Intelligent Buildings" 
 IMA Journal of Mathematical Control and Information, Vol. 27, pp. 527543, 2010. 

Abstract
BibTeX
The aim of this paper is to propose a modelbased feedback control strategy for indoor temperature regulation
in buildings equipped with underfloor air distribution (UFAD). Supposing distributed sensing and
actuation capabilities, a 0D model of the ventilation process is derived, based on the thermodynamics
properties of the flow. A statespace description of the process is then inferred, including discrete events
and nonlinear components. The use of a wireless sensor network (WSN) and the resulting communication
constraints with the IEEE 802.15.4 standard are discussed. Both synchronous and asynchronous
transmissions are considered. Based on the linear part of the model, different H¥ robust multipleinput
multipleoutput (MIMO) controllers are designed, first with a standard mixedsensitivity approach and
then by taking into account the networkinduced delay explicitly. The impact of the communication constraints
and the relative performances of the controllers are discussed based on simulation results.
@article{WiMaPaBri:ima10,
author = "E.~Witrant and P.~Di~Marco and P.~Park and C.~Briat",
title = "Limitations and Performances of Robust Control over WSN: UFAD Control in Intelligent Buildings",
year = "2010",
journal = "IMA Journal of Mathematical Control and Information"
volume = "27"
pages = "527543"
}



38.  Corentin Briat, Olivier Sename and JeanFrançois Lafay 
 "Memory Resilient Gainscheduled StateFeedback Control of Uncertain LTI/LPV TimeDelay Systems with TimeVarying Delays" 
 Systems & Control Letters, Vol. 59(8), pp. 451459, 2010 

Abstract
BibTeX
The stabilization of uncertain LTI/LPV
time delay systems with time varying delays by
statefeedback controllers is addressed. At the difference of other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to
uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exactmemory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow to check the stability of the closedloop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the $\mathcal{H}_\infty$ performance measure is considered. The interest of the approach is finally illustrated through several examples.
@article{Briat:aut09,
author = "C.~Briat and O.~Sename and JF.~Lafay",
title = "Memory Resilient Gainscheduled StateFeedback Control of Uncertain {LTI/LPV} TimeDelay Systems with TimeVarying Delays",
year = "2010",
journal = "Systems \& Control Letters"
volume = "59(8)"
pages = "451459"
}



39.  Corentin Briat and Erik I. Verriest 
 "A New DelaySIR Model for Pulse Vaccination" 
 Biomedical Signal Processing and Control, Vol. 4, pp. 272277, 2009 

Abstract
BibTeX
This paper introduces a new model for disease outbreaks. This model
describes the disease evolution through a system of nonlinear
differential equations with distributeddelay. The main difference
between classical SIRmodel resides in the fact that the recovery
rate of the population is expressed as a distributeddelay term
modeling the time spent being sick by infected people. This model is
identified to fit realistic measurements which shows the
effectiveness of the model. Finally, we develop an optimal campaign
vaccination strategy based on recent results on the impulsive
control of timedelay systems.
@article{Briat:bspc09,
author = "C.~Briat and E.~I.~Verriest",
title = "A New DelaySIR Model for Pulse Vaccination",
year = "2009",
journal = "Biomedical Signal Processing and Control",
volume = "4",
pages = "272277",
}



40.  Corentin Briat, Olivier Sename and JeanFrançois Lafay 
 "\(\mathcal{H}_\infty\) delayscheduled control of linear systems with timevarying delays" 
 IEEE Transactions on Automatic Control, Vol. 42(8), pp. 22502260, 2009 

Abstract
BibTeX
This paper deals with \(\mathcal{H}_\infty\) delayscheduled control of linear systems with
timevarying delays. First, we introduce a new model
transformation which allows us to provide an unified approach in the framework of linear parameter varying systems, to analyze
stability and design statefeedback controllers. Second, we
extend this method to develop a new type of controller where the statefeedback is timevarying and scheduled by the value of the delay (delayscheduled controllers). All the results are provided
in terms of Linear Matrix Inequalities (LMIs).
@article{Briat:tac09,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "$\mathcal{H}_\infty$ delayscheduled control of linear systems with timevarying delays",
year = "2009",
journal = "{IEEE} Transactions on Automatic Control",
volume = "42(8)",
pages = "22552260",
}



41.  Corentin Briat, Olivier Sename and JeanFrançois Lafay 
 "DelayScheduled StateFeedback Design for TimeDelay Systems with TimeVarying Delays  A LPV Approach" 
 Systems & Control Letters, Vol. 58(9), pp. 664671, 2009 

Abstract
BibTeX
This paper is concerned in the synthesis of delayscheduled
statefeedback stabilizing linear systems with timevarying delay
when the delay can be approximatively known in realtime. First we
introduce a new model transformation turning the timedelay system
into an uncertain LPV system. Using this reformulation we elaborate
delaydependent stability test based on the socalled fullblock
\(\mathcal{S}\)procedure and derive from it a delaydependent
stabilization lemma. Our results are then relaxed using a new
relaxation lemma which is shown to have good properties and provide
then LMI based theorems, wellknown for their tractability. Our
results tackle error measurement on the delay. We show the
efficiency of the method through an example.
@article{Briat:scl09,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "DelayScheduled StateFeedback Design for TimeDelay Systems with TimeVarying Delays  A LPV Approach",
year = "2009",
journal = "Systems \& Control Letters",
volume = "58(9)",
pages = "664671",
}
