Journal papers

1. Corentin Briat
"Stability and performance analysis of linear positive systems with delays using input-output methods"
International Journal of Control (in press)
Abstract BibTeX
It is known that input-output approaches based on scaled small-gain theorems with constant \(D\)-scalings and integral linear constraints are non-conservative 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 input-output 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 time-invariant/-varying delays and linear difference equations. In particular, we give a simple proof for the characterization of diagonal Riccati stability for systems with discrete-delays 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 input-output 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 input-output methods",
journal = "International Journal of Control (in press)",
volume = "",
pages = "",
year = "2017",
}


2. Corentin Briat
"Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems"
Nonlinear Analysis: Hybrid Systems, Vol. 24, pp. 198-226, 2017.
Abstract BibTeX
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise decrease of a linear copositive Lyapunov function and are formulated in terms of finite-dimensional or semi-infinite 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 infinite-dimensional 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 = "Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems",
journal = "Nonlinear Analysis: Hybrid Systems",
volume = "24",
pages = "198--226",
year = "2017",
}


3. Corentin Briat
"Sign properties of Metzler matrices with applications"
Linear Algebra and Its Applications, Vol. 515, pp. 53-86, 2017.
Abstract BibTeX
Several results about sign properties of Metzler matrices are obtained. It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms the negativity of the diagonal elements of the Metzler sign-matrix and the acyclicity of the associated directed graph. Similar results are obtained for the case of Metzler block-matrices and Metzler mixed-matrices, the latter being a class of Metzler matrices containing both sign- and real-type entries. The problem of assessing the sign-stability 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 sign-stability is then generalized to the concept of Ker_+(B)\)-sign-stability, a problem that arises in the analysis of certain jump Markov processes. A sufficient condition for the Ker\(_+(B)\)-sign-stability of Metzler sign-matrices is obtained and formulated using inverses of sign-matrices 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 = "53--86",
year = "2017",
}


4. Corentin Briat
"Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints"
Automatica, Vol. 74, pp. 279-287, 2016
Abstract BibTeX
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting. The concepts of mean-square stability and dwell-times are utilized in order to formulate relevant stability conditions for such systems. These conditions are formulated as convex clock-dependent 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 dwell-time conditions are obtained and non-conservatively turned into state-feedback stabilization conditions. The results are finally applied to the analysis and control of stochastic sampled-data 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 sampled-data systems under dwell-time constraints",
journal = "Automatica",
volume = "74",
pages = "279--287",
year = "2016",
}


5. Corentin Briat and Mustafa Khammash
"Interval peak-to-peak observers for continuous- and discrete-time systems with persistent inputs and delays"
Automatica, Vol. 74, pp. 206-213, 2016
Abstract BibTeX
While the design of optimal peak-to-peak 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 non-conservative approach formulated in terms of a tractable finite-dimensional linear program for designing a class of interval observers achieving minimum peak-to-peak 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 time-delay and discrete-time 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 peak-to-peak observers for continuous/discrete-time systems with persistent inputs and delays",
journal = "Automatica",
volume = "74",
pages = "206--213",
year = "2016",
}


6. 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. 1108-1116, 2016
Abstract BibTeX
The design and implementation of regulation motifs ensuring robust perfect adaptation are challenging problems in synthetic biology. Indeed, the design of high-yield 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 = "1108--1116",
year = "2016",
}


7. Corentin Briat
"Theoretical and numerical comparisons of looped functionals and clock-dependent Lyapunov functions—The case of periodic and pseudo-periodic systems with impulses"
International Journal of Robust and Nonlinear Control, Vol. 26(10), pp. 2232-2255, 2016
Abstract BibTeX
The stability of uncertain periodic and pseudo-periodic systems with impulses is analyzed in the looped-functional and clock-dependent Lyapunov function frameworks. These alternative and equivalent ways for characterizing discrete-time 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 non-restrictive class of state-feedback controllers are also provided. The obtained results readily extend to uncertain impulsive periodic and pseudo-periodic systems, a generalization of periodic systems that admit changes in the ‘period’ from one pseudo-period to another. The obtained conditions are expressed as infinite-dimensional 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 clock-dependent Lyapunov functions when a particular structure for the looped functional is considered. The conclusion is that the approach based on clock-dependent 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 clock-dependent Lyapunov functions—The case of periodic and pseudo-periodic systems with impulses",
journal = "International Journal of Robust and Nonlinear Control",
volume = "26(10)",
pages = "2232--2255",
year = "2016",
}


8. 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. 17-28, 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 = "17--28",
year = "2016",
}


9. 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. 811-816, 2016
Abstract BibTeX
In this technical note, the stability and failure tolerant control are investigated for linear time-invariant (LTI) control systems with occasional controller failures. At first, a collection of non-convex 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 time-scheduled Lyapunov function approach is considered and alternative convex conditions are obtained. Based on this result, a time-dependent failure-tolerant 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 = "811--816",
year = "2016",
}


10. Corentin Briat
"Stability analysis and control of a class of LPV systems with piecewise constant parameters"
Systems & Control Letters, Vol. 82, pp. 10-17, 2015
Abstract BibTeX
Stability criteria characterizing the asymptotic stability of a class of LPV systems with piecewise constant parameters under constant and minimum dwell-time are derived. It is shown that, for such systems, the conditions for the stability under minimum dwell-time 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 time-dependent gain-scheduled state-feedback 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 = "10--17",
year = "2015",
}


11. Corentin Briat and Alexandre Seuret
"On the necessity of looped-functionals arising in the analysis of pseudo-periodic, sampled-data and hybrid systems"
International Journal of Control, Vol. 88(12), pp. 2563-2569, 2015
Abstract BibTeX
Looped-functionals 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 sampled-data, impulsive and switched systems have only been shown to be sufficient for the characterisation of their associated discrete-time 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 pseudo-periodic systems, that encompass periodic, impulsive, sampled-data and switched systems as special cases.
@article{Briat:15IJC,
author = "C. Briat and A. Seuret",
title = "On the necessity of looped-functionals arising in the analysis of pseudo-periodic, sampled-data and hybrid systems",
journal = "Systems \& Control Letters",
volume = "88(12)",
pages = "2563--2569",
year = "2015",
}


12. Corentin Briat
"Convex conditions for the robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time"
Systems & Control Letters, Vol. 78, pp. 63-72, 2015
Abstract BibTeX
Alternative conditions for establishing dwell-time 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 time-varying uncertainties. The low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state-feedback 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 looped-functionals 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 time-scaling, emphasizing that the complexity of the approach does not depend on the size of the dwell-time. 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 mode-dependent dwell-time",
journal = "Systems \& Control Letters",
volume = "78",
pages = "63--72",
year = "2015",
}


13. Alexandre Seuret and Corentin Briat
"Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals"
Automatica, Vol. 55, pp. 274-278, 2015.
Abstract BibTeX
The robust stability analysis of asynchronous and uncertain sampled-data systems with constant incremental input delay is addressed in the looped-functional framework. These functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete-time stability conditions in an affine way, enabling then the consideration of uncertain and time-varying systems. The stability conditions are obtained by first reformulating the sampled-data system as an impulsive system, and by then considering a tailored looped-functional 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 sampled-data systems with incremental delay using looped-functionals",
journal = "Automatica",
volume = "55",
pages = "274--278",
year = "2015",
}


14. 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. 851-865, 2015
Abstract BibTeX
We derive a modular fluid-flow 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 packet-level 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 = "851--865",
year = "2015",
}


15. Ankit Gupta, Corentin Briat and Mustafa Khammash
"A scalable computational framework for establishing long-term 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 well-established 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 long-term 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, well-known 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 non-ergodic biological network are also discussed.
@article{Briat:14PLOS,
author = "A. Gupta and C. Briat and M. Khammash",
title = "A scalable computational framework for establishing long-term behavior of stochastic reaction networks",
journal = "PLOS Computational Biology",
year = "2014",
volume = "10(6)",
pages="e1003669",
url="http://arxiv.org/abs/1304.5404",
}


16. Corentin Briat
"Convex lifted conditions for robust \(ll_2\)-stability analysis and \(ll_2\)-stabilization of linear discrete-time switched systems with minimum dwell-time constraint"
Automatica, Vol. 50(3), pp. 976-983, 2014
Abstract BibTeX
Stability analysis of discrete-time switched systems under minimum dwell-time 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 l2-gain 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 discrete-time switched systems with minimum dwell-time constraint",
journal = "Automatica",
volume = "50(3)",
pages = "976--983",
year = "2014",
}


17. Corentin Briat
"Spectral necessary and sufficient conditions for sampling-period-independent stabilization of periodic and aperiodic sampled-data systems using a class of generalized sampled-data hold functions"
International Journal of Control, Vol. 87(3), pp. 612-621, 2014
Abstract BibTeX
Sampling-period-independent (SPI) stabilization of both periodic and aperiodic sampled-data systems using a class of generalized sampled-data hold functions is addressed. It is proved that for this specific class of hold functions, a continuous-time linear system with rank-minimal input matrix and with non-defective eigenvalues on the imaginary axis is SPI-stabilizable if and only if the spectrum of the system is contained in the closed left-half plane. A systematic procedure for constructing suitable state-feedback controllers is also provided. Several examples are finally discussed for illustration.
@article{Briat:14ijc,
author = "C. Briat",
title = "Spectral necessary and sufficient conditions for sampling-period-independent stabilization of periodic and aperiodic sampled-data systems using a class of generalized sampled-data hold functions",
journal = "International Journal of Control",
volume = "87",
issue = "3",
pages = "612--621",
year = "2014",
}


18. Corentin Briat
"Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints"
Automatica, Vol. 49(11), pp. 3349-3457, 2013
Abstract BibTeX
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying 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 dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively 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 state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data 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 sampled-data systems under dwell-time constraints",
journal = "Automatica",
volume = "49(11)",
pages = "3449-3457",
year = "2013",
}


19. Burak Demirel, Corentin Briat and Mikael Johansson
"Deterministic and Stochastic Approaches to Supervisory Control Design for Networked Systems with Time-Varying Communication Delays"
Nonlinear Analysis: Hybrid Systems, Vol. 10, pp. 94-110, 2013
Abstract BibTeX
This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the closed-loop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwell-time switching and is based on a novel multiple Lyapunov-Krasovskii functional. We develop stability conditions that can be verified by semi-definite 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 large-scale 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 Time-Varying Communication Delays",
journal = "Nonlinear Analysis: Hybrid Systems",
year = "2013",
volume = "10",
pages ="94--110",
}


20. 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. 1932-1954, 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 supply-rates 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 ="1932--1954",
}


21. Corentin Briat and Alexandre Seuret
"Affine characterizations of minimal and mode-dependent dwell-times for uncertain linear switched systems"
IEEE Transactions on Automatic Control, Vol. 58(5), pp. 1304-1310, 2013.
Abstract BibTeX
An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwell-time. These conditions are expressed as infinite-dimensional LMIs which can be solved using recent polynomial optimization techniques such as sum-of-squares. The specific structure of the conditions is finally utilized in order to derive dwell-time 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 mode-dependent dwell-times for uncertain linear switched systems",
journal = "{IEEE} Transactions on Automatic Control",
year = "2013",
volume ="58(5)",
pages ="1304--1310",
}


22. Corentin Briat and Olivier Sename
"Discussion on "Time-delay model-based control of the glucose-insulin system, by means of a state observer""
European Journal of Control, Vol. 18(6), pp. 607-609, 2012


23. Corentin Briat and Alexandre Seuret
"Convex dwell-time characterizations for uncertain linear impulsive systems"
IEEE Transactions on Automatic Control, Vol. 57(12), pp. 3241-3246, 2012
Abstract BibTeX
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve non-monotonically 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 dwell-time characterizations for uncertain linear impulsive systems",
journal = "{IEEE} Transactions on Automatic Control",
volume ="57(12)",
pages ="3241--3246",
year = "2012",
}


24. Corentin Briat and Alexandre Seuret
"A looped-functional approach for robust stability analysis of linear impulsive systems"
Systems & Control Letters, Vol. 61, pp. 980-988, 2012
Abstract BibTeX
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwell-times 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 sampled-data systems, illustrate the efficiency of the approach.
@article{Briat:12scl,
author = "C. Briat and A. Seuret",
title = "A looped-functional approach for robust stability analysis of linear impulsive systems",
journal = "Systems & Control Letters",
pages ="980--988",
volume ="61",
year = "2012",
}


25. Corentin Briat, Olivier Sename and Jean-François Lafay
"Design of LPV observers for LPV Time-Delay Systems: An Algebraic Approach"
International Journal of Control, Vol. 84(9), pp. 1533-1542, 2012
Abstract BibTeX
The design of reduced-order observer for LPV time-delay 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 LMI-based approaches are provided to select an observer within this family according to some criterion; e.g. maximization of the delay-margin 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 J-F.~Lafay",
title = "Design of LPV observers for LPV Time-Delay Systems: An Algebraic Approach",
year = "2011",
journal = "International Journal of Control"
volume ="84(9)",
pages ="1533--1542",
url="http://dx.doi.org/10.1080/00207179.2011.611950",
}


26. Corentin Briat
"Convergence and Equivalence results for the Jensen's inequality - Application to time-delay and sampled-data systems"
IEEE Transactions on Automatic Control, Vol. 56(7), pp. 1660-1665, 2011
Abstract BibTeX
The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data 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. Non-uniform 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 well-posedness 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 time-delay and sampled-data systems",
year = "2011",
journal = "IEEE Transactions on Automatic Control",
url = "http://dx.doi.org/10.1109/TAC.2011.2121410",
pages = "1660--1665",
volume = "56(7)",
}


27. 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. 527-543, 2010.
Abstract BibTeX
The aim of this paper is to propose a model-based 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 state-space 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 multiple-input multiple-output (MIMO) controllers are designed, first with a standard mixed-sensitivity approach and then by taking into account the network-induced 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 = "527--543"
}


28. Corentin Briat, Olivier Sename and Jean-François Lafay
"Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Time-Delay Systems with Time-Varying Delays"
Systems & Control Letters, Vol. 59(8), pp. 451-459, 2010
Abstract BibTeX
The stabilization of uncertain LTI/LPV time delay systems with time varying delays by state-feedback 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 exact-memory 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 closed-loop 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 J-F.~Lafay",
title = "Memory Resilient Gain-scheduled State-Feedback Control of Uncertain {LTI/LPV} Time-Delay Systems with Time-Varying Delays",
year = "2010",
journal = "Systems \& Control Letters"
volume = "59(8)"
pages = "451--459"
}


29. Corentin Briat and Erik I. Verriest
"A New Delay-SIR Model for Pulse Vaccination"
Biomedical Signal Processing and Control, Vol. 4, pp. 272-277, 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 distributed-delay. The main difference between classical SIR-model resides in the fact that the recovery rate of the population is expressed as a distributed-delay 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 time-delay systems.
@article{Briat:bspc09,
author = "C.~Briat and E.~I.~Verriest",
title = "A New Delay-SIR Model for Pulse Vaccination",
year = "2009",
journal = "Biomedical Signal Processing and Control",
volume = "4",
pages = "272-277",
}


30. Corentin Briat, Olivier Sename and Jean-François Lafay
"\(\mathcal{H}_\infty\) delay-scheduled control of linear systems with time-varying delays"
IEEE Transactions on Automatic Control, Vol. 42(8), pp. 2250-2260, 2009
Abstract BibTeX
This paper deals with \(\mathcal{H}_\infty\) delay-scheduled control of linear systems with time-varying 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 state-feedback controllers. Second, we extend this method to develop a new type of controller where the state-feedback is time-varying and scheduled by the value of the delay (delay-scheduled 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 = "$\mathcal{H}_\infty$ delay-scheduled control of linear systems with time-varying delays",
year = "2009",
journal = "{IEEE} Transactions on Automatic Control",
volume = "42(8)",
pages = "2255-2260",
}


31. Corentin Briat, Olivier Sename and Jean-François Lafay
"Delay-Scheduled State-Feedback Design for Time-Delay Systems with Time-Varying Delays - A LPV Approach"
Systems & Control Letters, Vol. 58(9), pp. 664-671, 2009
Abstract BibTeX
This paper is concerned in the synthesis of delay-scheduled state-feedback stabilizing linear systems with time-varying delay when the delay can be approximatively known in real-time. First we introduce a new model transformation turning the time-delay system into an uncertain LPV system. Using this reformulation we elaborate delay-dependent stability test based on the so-called full-block \(\mathcal{S}\)-procedure and derive from it a delay-dependent 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, well-known 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 = "Delay-Scheduled State-Feedback Design for Time-Delay Systems with Time-Varying Delays - A LPV Approach",
year = "2009",
journal = "Systems \& Control Letters", volume = "58(9)",
pages = "664-671",

}