Conference papers

1. Corentin Briat and Mustafa Khammash
"Robust and structural ergodicity analysis of stochastic biomolecular networks involving synthetic antithetic integral controllers" (slides), 20th IFAC World Congress, Toulouse, France, 2017
Abstract BibTeX
Ergodicity and output controllability have been shown to be fundamental concepts for the analysis and synthetic design of closed-loop stochastic reaction networks, as exemplified by the use of antithetic integral feedback controllers. In [Gupta, Briat \& Khammash, PLoS Comput. Biol., 2014], some ergodicity and output controllability conditions for unimolecular and certain classes of bimolecular reaction networks were obtained and formulated through linear programs. To account for context dependence, these conditions were later extended in [Briat \& Khammash, CDC, 2016] to reaction networks with uncertain rate parameters using simple and tractable, yet potentially conservative, methods. Here we develop some exact theoretical methods for verifying, in a robust setting, the original ergodicity and output controllability conditions based on algebraic and polynomial techniques. Some examples are given for illustration.
@inproceedings{Briat:16ifac1,
author= "C. Briat and M. Khammash",
title= "Robust and structural ergodicity analysis of stochastic biomolecular networks involving synthetic antithetic integral controllers",
booktitle="20th IFAC World Congress",
year= "2017",
address = "Toulouse, France",
pages = "11405--11410",
}


2. Corentin Briat and Mustafa Khammash
"Simple interval observers for linear impulsive systems with applications to sampled-data and switched systems" (slides), 20th IFAC World Congress, Toulouse, France, 2017
Abstract BibTeX
Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The proposed approach is fully constructive in the sense that suitable observer gains can be extracted from the solution of the optimization problems and is flexible enough to be extended to include performance constraints and parametric uncertainties. In order to be solvable, the infinite-dimensional linear programs are relaxed using a method based on sum of squares which is known to be asymptotically exact in the present case. Three examples are given for illustration: the first one pertains on the interval observation of an impulsive system under a minimum dwell-time constraint, the second one is about the interval observation of an aperiodic sampled-data system and the last one is about the interval observation of a linear switched system.
@inproceedings{Briat:16ifac2,
author= "C. Briat and M. Khammash",
title= "Simple interval observers for linear impulsive systems with applications to sampled-data and switched systems",
booktitle="20th IFAC World Congress",
year= "2017",
address = "Toulouse, France",
pages = "5235--5240",
}


3. Corentin Briat and Mustafa Khammash
"Stability analysis of LPV systems with piecewise differentiable parameters" (slides), 20th IFAC World Congress, Toulouse, France, 2017
Abstract BibTeX
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of hybrid systems. The underlying idea is to reformulate the considered LPV system as an 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. Then, using a result pertaining on the stability of hybrid systems, two stability conditions are established and shown to naturally generalize and unify the well-known quadratic and robust stability criteria together. The obtained conditions being infinite-dimensional, a relaxation approach based on sum of squares programming is used in order to obtain tractable finite-dimensional conditions. The approach is finally illustrated on two examples from the literature.
@inproceedings{Briat:16ifac3,
author= "C. Briat and M. Khammash",
title= "Stability analysis of LPV systems with piecewise differentiable parameters",
booktitle="20th IFAC World Congress",
year= "2017",
address = "Toulouse, France",
pages = "7815--7820",
}


4. Corentin Briat and Mustafa Khammash
"Robust ergodicity and tracking in antithetic integral control of stochastic biochemical reaction networks" (slides), 55th IEEE Conference on Decision and Control, Las Vegas, USA, 2016
Abstract BibTeX
Controlling stochastic reactions networks is a challenging problem with important implications in various fields such as systems and synthetic biology. Various regulation motifs have been discovered or posited over the recent years, the most recent one being the so-called Antithetic Integral Control (AIC) motif in Briat et al. (Cell Systems, 2016). 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 two different approaches. The first one is quantitative and relies on the notion of interval matrices while the second one is qualitative and is based on sign properties of matrices. The obtained results lie in the same spirit as those obtained in Briat et al. (Cell Systems, 2016) where properties of reaction networks are independently characterized in terms of control theoretic concepts, linear programming conditions and graph theoretic conditions.
@inproceedings{Briat:15cdc,
author= "C. Briat and M. Khammash",
title= "Robust ergodicity and tracking in antithetic integral control of stochastic biochemical reaction networks",
booktitle="55th IEEE Conference on Decision and Control",
year= "2016",
address = "Las Vegas, USA",
pages = "752--757",
}


5. Sei Zhen Khong, Corentin Briat and Anders Rantzer
"Positive systems analysis via integral linear constraints" (slides), 54th IEEE Conference on Decision and Control, Osaka, Japan, 2015
Abstract BibTeX
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees feedback positivity. Furthermore, the notion of integral linear constraints (ILC) is utilised as a tool to characterise uncertainty in positive feedback systems. Robustness analysis of positive linear time-varying and nonlinear feedback systems is studied using ILC, paralleling the well-known results based on integral quadratic constraints.
@inproceedings{Briat:15cdc,
author= "S. Z. Khong and C. Briat and A. Rantzer",
title= "Positive systems analysis via integral linear constraints",
booktitle="54th IEEE Conference on Decision and Control",
year= "2015",
address = "Osaka, Japan",
pages = "6373--6378",
}


6. Igor Pontes Duff, Pierre Vuillemin, Charles Poussot-Vassal, Corentin Briat and Cédric Seren
"Approximation of stability regions for large-scale time-delay systems using model reduction techniques" (slides), 14th European Control Conference, Linz, Austria, 2015
Abstract BibTeX
In this paper, the problem of determining the approximate stability regions of large-scale time-delay systems (LS TDS) is solved using model approximation techniques. To achieve this, an \(\mathcal{H}_2\) -oriented approximation algorithm, referred to as TF-IRKA, is considered. This algorithm has been shown to be well suited for the approximation of infinite- dimensional systems into finite-dimensional ones. We show here how model reduction can be used to approximate time- delay systems with multiple delays and obtain a fairly accurate estimation of their stability regions. Discussions regarding the adaptation of existing algorithms to the considered problem are also provided. Several numerical examples illustrate the efficiency and accuracy of the approach.
@inproceedings{Briat:15ecc,
author= " I. {Pontes Duff} and P. Vuillemin and C. {Poussot-Vassal} and C. Briat and C. Seren",
title= "Approximation of stability regions for large-scale time-delay systems using model reduction techniques",
booktitle="14th European Control Conference",
year= "2015",
address = "Linz, Austria",
pages = "",
}


7. Corentin Briat, Ankit Gupta and Mustafa Khammash
"A Control Theory for Stochastic Biomolecular Regulation" (slides), SIAM Conference on Control Theory and its Applications, Paris, France, 2015
Abstract BibTeX
@inproceedings{Briat:CTA15,
author= "C. Briat and A. Gupta and M. Khammash",
title= "A Control Theory for Stochastic Biomolecular Regulation",
booktitle="SIAM Conference on Control Theory and its Applications",
year= "2015",
address = "Paris, France",
pages = "",
}


8. Igor Pontes Duff, Pierre Vuillemin, Charles Poussot-Vassal, Cédric Seren and Corentin Briat
"Stability and performance analysis of large-scale aircraft vibration delay model using model reduction techniques", EuroGNC, Toulouse, France, 2015
Abstract BibTeX
In this paper, the problem estimate stability and computing the frequency-limited \(\mathcal{H}_{2,\Omega}\) performances of an anti-vibration controller subject to feedback time delays is considered. The contribution of this paper lies in the application of realization-less model reduction techniques on a large-scale aeroservoelastic aircraft model subject to delays in order to obtain a representative simpler model for which the stability and performance metrics can be efficiently computed.
@inproceedings{Briat:15GNC,
author= " I. {Pontes Duff} and P. Vuillemin and C. {Poussot-Vassal} and C. Seren and C. Briat",
title= "Stability and performance analysis of large-scale aircraft vibration delay model using model reduction techniques",
booktitle="EuroGNC",
year= "2015",
address = "Toulouse, France",
pages = "",
}


9. Alexandre Seuret, Corentin Briat and Frédéric Gouaisbaut
"Stability analysis of asynchronous sampled-data systems with discrete-time constant input delay" (slides), 53rd IEEE Conference on Decision and Control, Los Angeles, USA, 2014
Abstract BibTeX
Aperiodic sampled-data systems controlled by a delayed state-feedback controller arise naturally in networked control systems. We propose a novel way to analyze the stability of sampled-data systems with discrete-time constant input delay by, first, reformulating the system into an aperiodic discrete-time system with constant delay and by, then, considering a mixture of a discrete-time Lyapunov-Krasovskii functional and a looped-functional in order to account for the presence of the delay and the sampling aperiodicity, respectively. Stability criteria, expressed as linear matrix inequalities, are derived for both certain and uncertain (time-varying) systems. An example is given for illustration.
@inproceedings{Briat:14cdc,
author= "A. Seuret and C. Briat and F. Gouaisbaut",
title= "Stability analysis of asynchronous sampled-data systems with discrete-time constant input delay",
booktitle="53rd IEEE Conference on Decision and Control",
year= "2014",
address = "Los Angeles, USA",
pages = "4342--4347",
}


10. Corentin Briat, Ankit Gupta, Iman Shames and Mustafa Khammash
"Scalable tests for ergodicity analysis of large-scale interconnected stochastic reaction networks" (slides), 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, The Netherlands, 2014
Abstract BibTeX
@inproceedings{Briat:14mtns,
author= "C. Briat, A. Gupta, I. Shames and M. Khammash",
title= "Scalable tests for ergodicity analysis of large-scale interconnected stochastic reaction networks",
booktitle="21st International Symposium on Mathematical Theory of Networks and Systems",
year= "2014",
address = "Groningen, The Netherlands",
pages = "92--95",
}


11. Corentin Briat and Mustafa Khammash
"Integral population control of a quadratic dimerization process" (slides), 52nd IEEE Conference on Decision and Control, Florence, Italy, 2013.
Abstract BibTeX
Moment control of a simple quadratic reaction network describing a dimerization process is addressed. 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 upper-bound of the variance of the monomer species, acting on the system as unknown input due to the moment openness, is obtained. The obtained results are illustrated by an example relying on the simulation of a cell population using stochastic simulation algorithms.
@inproceedings{Briat:13cdc,
author= "C. Briat and M. Khammash",
title= "Integral population control of a quadratic dimerization process",
booktitle="52nd IEEE Conference on Decision and Control, Florence, Italy",
year= "2013",
pages = "3367--3372",
}


12. Corentin Briat and Mustafa Khammash
"Computer control of gene expression: Robust setpoint tracking of protein mean and variance using integral feedback" (slides), 51st IEEE Conference on Decision and Control, Maui, Hawaii, USA, 2012.
Abstract BibTeX
Protein mean and variance levels in a simple stochastic gene expression circuit are controlled using proportional integral feedback. 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 necessary and 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. Simulation examples illustrate the results.
@inproceedings{Briat:12cdc,
author= "C. Briat and M. Khammash",
title= "Computer control of gene expression: Robust setpoint tracking of protein mean and variance using integral feedback",
booktitle="51st IEEE Conference on Decision and Control, Maui, Hawaii, USA",
year= "2012",
pages = "3582--3588",
}


13. Corentin Briat and Alexandre Seuret
"Robust stability of impulsive systems: A functional-based approach" (slides), 4th IFAC Conference on analysis and design of hybrid systems (ADHS'12), Eindhoven, the Netherlands, 2012.
Abstract BibTeX
An improved functional-based approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov looped-functionals is provided. Looped functionals are particular functionals that allow to encode discrete-time stability criteria into continuous-time conditions and to consider non-monotonic Lyapunov functions along the trajectories of the impulsive system. Unlike usual discrete-time stability conditions, the obtained ones are convex in the system matrices, an important feature for extending the results to uncertain systems. It is emphasized in the examples that the proposed approach can be applied to a class of systems for which existing approaches are inconclusive, notably systems having unstable continuous and discrete dynamics.
@inproceedings{Briat:12adhs2,
author= "C. Briat and A. Seuret",
title= "Robust stability of impulsive systems: A functional-based approach",
booktitle="4th IFAC Conference on analysis and design of hybrid systems (ADHS'12), Eindhoven, the Netherlands, 2012",
year= "2012",
pages = "412--417",
}


14. Burak Demirel, Corentin Briat and Mikael Johansson
"Supervisory Control Design for Networked Systems with Time-Varying Communication Delays" (slides), 4th IFAC Conference on analysis and design of hybrid systems (ADHS'12), Eindhoven, the Netherlands, 2012.
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 analysis conditions that can be verified by semi-definite programming, and show that associated state feedback synthesis problem also can be solved using convex optimization. A wide-area power control application is used to illustrate the effectiveness of our approach.
@inproceedings{Briat:12adhs1,
author= "B. Demirel and C. Briat and M. Johansson",
title= "Supervisory Control Design for Networked Systems with Time-Varying Communication Delays",
booktitle="4th IFAC Conference on analysis and design of hybrid systems (ADHS'12), Eindhoven, the Netherlands, 2012",
year= "2012",
pages = "133--140",
}


15. Corentin Briat, Emre Altug Yavuz and Gunnar Karlsson
"A conservation-law-based modular fluid-flow model for network congestion modeling" (slides), 31st IEEE International Conference on Computer Communications (INFOCOM'12), Orlando, Florida, USA, 2012
Abstract BibTeX
A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of network elements such as queues, users, and transmission channels, and network description variables, including sending/acknowledgement rates and delays, are inferred from this law and obtained by applying this principle locally. The modularity of the devised model makes it sufficiently generic to describe any network topology, and appealing for building simulators. Previous models in the literature are often not capable of capturing the transient behavior of the network precisely, making the resulting analysis inaccurate in practice. Those models can be recovered from exact reduction or approximation of this new model. An important aspect of this particular modeling approach is the introduction of new tight building blocks that implement mechanisms ignored by the existing ones, notably at the queue and user levels. Comparisons with packet-level simulations corroborate the proposed model.
@inproceedings{Briat:12infocom,
author= "C. Briat and E. A. Yavuz and G. Karlsson",
title= "A conservation-law-based modular fluid-flow model for network congestion modeling",
booktitle="31st {IEEE} International Conference on Computer Communications (INFOCOM'12), Orlando, Florida, USA",
year= "2012",
pages = "2050--2058",
}


16. Corentin Briat
"Robust stability analysis of uncertain Linear Positive Systems via Integral Linear Constraints: \(L_1\)- and \(L_\infty\)-gains characterizations" (slides), 50th IEEE Conference on Decision and Control, Orlando, Florida, USA, 2011
Abstract BibTeX
Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustness and performance analysis and lead to \(L_1\)- and \(L_\infty\)-gains characterizations. This naturally guides to the definition of Integral Linear Constraints (ILCs) for the characterization of input-output nonnegative uncertainties. It turns out that these integral linear constraints can be linked to the Laplace domain, in order to be tuned adequately, by exploiting the \(L_1\)-norm and input/output signals properties. This dual viewpoint allows to prove that the static-gain of the uncertainties, only, is critical for stability. This fact provides a new explanation for the surprising stability properties of linear positive time-delay systems. The obtained stability and performance analysis conditions are expressed in terms of (robust) linear programming problems that are transformed into finite dimensional ones using the Handelman's Theorem. Several examples are provided for illustration.
@inproceedings{Briat:11cdc3,
author= "Corentin~Briat",
title= "Robust stability analysis of uncertain Linear Positive Systems via Integral Linear Constraints: $\mathcal{L}_1$- and $\mathcal{L}_\infty$-gains characterizations",
booktitle="50th IEEE Conference on Decision and Control, Orlando, USA",
year= "2011",
pages = "3122--3129",
}


17. Corentin Briat
"Robust stability analysis in the *-norm and Lyapunov-Razumikhin functions for the stability analysis and control of time-delay systems" (slides), 50th IEEE Conference on Decision and Control, Orlando, Florida, USA, 2011
Abstract BibTeX
Lyapunov-Krasovskii functionals have been shown to have connections with input-output techniques considering delay operators mapping \(L_2\) to \(L_2\). It is shown here that Lyapunov-Razumikhin functions can also be connected to the input-output framework by considering operators on \(L_\infty\). Several important results from the Lyapunov-Razumikhin Theorem are retrieved and extended.
@inproceedings{Briat:11cdc2,
author= "Corentin~Briat",
title= "Robust stability analysis in the $*$-norm and Lyapunov-Razumikhin functions for the stability analysis and control of time-delay systems",
booktitle="50th IEEE Conference on Decision and Control, Orlando, USA",
year= "2011",
pages = "6319--6324",
}


18. Corentin Briat, Håkan Hjalmarsson, Gunnar Karlsson, Karl Henrik Johansson, Ulf T. Jönsson, Henrik Sandberg and Emre Altug Yavuz
"An axiomatic fluid-flow model for congestion control analysis" (slides), 50th IEEE Conference on Decision and Control, Orlando, Florida, USA, 2011
Abstract BibTeX
An axiomatic model for congestion control is derived. The proposed four axioms serve as a basis for the construction of models for the network elements. It is shown that, under some assumptions, some models of the literature can be recovered. A single-buffer/multiple-users topology is finally derived and studied for illustration.
@inproceedings{Briat:11cdc1,
author= "C.~Briat and H.~Hjalmarsson and K.H.~Johansson and G.~Karlsson and U.T.~{J"{o}nsson} and H.~Sandberg and E.A.~Yavuz",
title= "An axiomatic fluid-flow model for congestion control analysis",
booktitle="50th IEEE Conference on Decision and Control, Orlando, USA",
year= "2011",
pages = "3122--3129",
}


19. Yassine Ariba, Corentin Briat and Karl Henrik Johansson
"Simple conditions for L2 stability and stabilization of networked control systems" (slides), 18th IFAC World Congress, Milano, Italy, 2011.
Abstract BibTeX
The stability analysis and stabilization of networked control systems subject to data loss and time-varying transmission delays are explored. The stability result is based on quadratic separation and operator theory, which allows to capture the above phenomena into the single formalism of aperiodic sampling. The obtained stability condition is expressed through an LMI. The stabilization problem is a bit more involved due to the inherent structure of the obtained LMI. An approximation (dilation) is then proposed to obtain a more tractable LMI for stabilization. Several examples illustrate the effectiveness of the proposed approach.
@inproceedings{Briat:11,
author = "Y.~Ariba and C.~Briat and K. H. Johansson",
title = "Simple conditions for $ stability and stabilization of networked control systems",
year = "2011",
booktitle = "18th IFAC World Congress, Milano, Italy, 2011",
pages = "96--101",
}


20. Corentin Briat and Ulf T. Jönsson
"Dynamic equations on time-scale: application to stability analysis and stabilization of aperiodic sampled-data systems" (slides), 18th IFAC World Congress, Milano, Italy, 2011.
Abstract BibTeX
The stability analysis of systems with aperiodic sampling is analyzed in the framework of dynamic equations on time-scales. Lyapunov theory is used, with sample-period-dependent and independent Lyapunov functions, to obtain stability conditions expressed in terms of parameter dependent matrix inequalities. The examples illustrate the efficiency of the approach which is able to recover, for some systems, the theoretical results for the periodic sampling case even in the aperiodic case. It is also shown that some systems may have admissible varying sampling periods located in disjoint sets. Finally, stabilization results via switching state-feedback are provided; both robust and sampling-period-dependent controllers are considered. It is shown that the latter ones, using the information on the sampling period, can improve stability properties. Stabilization examples illustrate the effectiveness of the approach.
@inproceedings{Briat:11,
author = "C.~Briat and U. T.~{J"{o}nsson}",
title = "Dynamic equations on time-scale: application to stability analysis and stabilization of aperiodic sampled-data systems",
year = "2011",
booktitle = "18th IFAC World Congress, Milano, Italy, 2011",
pages = "11374--11379",
}


21. Corentin Briat and Alexandre Seuret
"Stability Criteria for Asynchronous Sampled-data Systems - A Fragmentation Approach" (slides), 18th IFAC World Congress, Milano, Italy, 2011.
Abstract BibTeX
The stability analysis of asynchronous sampled-data systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampled-data systems in a continuous-time framework via the use of peculiar functionals satisfying a necessary boundary condition. The method developed here is an extension of previous results using a fragmentation technique inspired from recent advances in time-delay systems theory. The approach leads to a tractable convex feasibility problem involving a small number of finite dimensional LMIs. The approach is then finally illustrated through several examples.
@inproceedings{Briat:11,
author = "C.~Briat and A.~Seuret",
title = "Stability Criteria for Asynchronous Sampled-data Systems - A Fragmentation Approach",
year = "2011",
booktitle = "18th IFAC World Congress, Milano, Italy, 2011",
pages = "1313--1318",
}


22. Corentin Briat and John Jairo Martinez-Molina
"\(\mathcal{H}_\infty\) Bounded Resilient state-feedback design for linear continuous-time systems - A robust control approach" (slides), 18th IFAC World Congress, Milano, Italy, 2011.
Abstract BibTeX
The quadratic stabilization of LTI systems by bounded resilient state-feedback controllers is addressed. The controllers are guaranteed to be non-fragile with respect to either uniform or nonuniform maximal implementation errors. The design of resilient controller relies on an LMI problem while boundedness of the coefficients (a NP-Hard problem) can be guaranteed by solving a nonconvex problem involving a BMI. The latter problem is solved using proposed locally convergent iterative LMI algorithms. Finally, an example is considered in order to illustrate the effectiveness of the approach.
@inproceedings{Briat:11,
author = "C.~Briat and J. J.~Martinez",
title = "$\mathcal{H}_\infty$ Bounded Resilient state-feedback design for linear continuous-time systems - A robust control approach",
year = "2011",
booktitle = "18th IFAC World Congress, Milano, Italy, 2011", pages = "9307--9312",

}


23. Corentin Briat, Emre Altug Yavuz and Gunnar Karlsson
"Impact of propagation delay estimation error on equilibrium and its stability" (slides), 10th International IFIP-TC6 Networking Conference, Valencia, Spain, 2011
Abstract BibTeX
Delay-based transmission control protocols need to separate round-trip time measurements into their constituting parts: the propagation and the queueing delays.We consider two means for this; the first is to take the propagation delay as the minimum observed RTT value, and the second is to measure the queueing delays by routers and feed them back to the sources. We choose FAST-TCP as a representative delay-based congestion avoidance protocol for analysis and study the impact of delay knowledge errors on the performance of the protocol. We have shown that while the first method destroys fairness and the uniqueness of the equilibrium, the stability of the protocol can easily be obtained through tuning the protocol terms appropriately. Even though the second technique is shown to preserve fairness and uniqueness of the equilibrium point, we have presented that unavoidable oscillations can occur around an equilibrium point
@inproceedings{Briat:11,
author= "C.~Briat and E. A.~Yavuz and G.~Karlsson",
title= "Impact of propagation delay estimation error on equilibrium and its stability",
booktitle="10th International IFIP-TC6 Networking Conference, Valencia, Spain",
year= "2011",
pages = "356--367",
}


24. Corentin Briat, Håkan Hjalmarsson, Gunnar Karlsson, Karl Henrik Johansson, Ulf T. Jönsson and Henrik Sandberg
"Nonlinear state-dependent delay modeling and stability analysis of internet congestion control" (slides), 49th IEEE Conference on Decision and Control, Atlanta, Georgia, USA, 2010
Abstract BibTeX
It is shown that the queuing delay involved in the closed-loop is state-dependent and does not depend on the current time. Then, using an accurate formulation for buffers, networks with arbitrary topologies can be built. At equilibrium, our model reduces to the widely used setup by Paganini et al. Using this model, the delay-derivative is analyzed and it is proved that the delay derivative does not exceed one for the considered topologies. It is then shown that the considered congestion control algorithm globally stabilizes a delay-free single buffer network. Finally, using a specific linearization result for systems with state-dependent delays from Cooke and Huang, we show the local stability of the single bottleneck network.
@inproceedings{Briat:10,
author= "C.~Briat and H.~Hjalmarsson and K.H.~Johansson and G.~Karlsson and U.T.~{J"{o}nsson} and H.~Sandberg",
title= "Nonlinear state-dependent delay modeling and stability analysis of internet congestion control",
booktitle="49th IEEE Conference on Decision and Control, Altlanta, USA",
year= "2010",
}


25. Corentin Briat and John Jairo Martinez-Molina
"Design of \(\mathcal{H}_\infty\) Bounded Non-Fragile Controllers for Discrete-Time Systems" (slides), 48th IEEE Conference on Decision and Control, Shanghai, China, 2009
Abstract BibTeX
This paper deals with the quadratic stabilization of discrete-time LTI systems using state-feedback controllers with bounded coefficients. The controllers are guaranteed to be non-fragile with respect to additive or multiplicative implementation errors. The approach is based on robust-control tools and LMIs. Finally, an example is given in order to illustrate the effectiveness of the approach.
@inproceedings{Briat:09e,
author = "C.~Briatand J. J~Martinez",
title = "Design of $\mathcal{H}_\infty$ Bounded Non-Fragile Controllers for Discrete-Time Systems",
year = "2009",
booktitle = "48th Conference on Decision and Control, Shanghai, China, 2009"
}


26. Corentin Briat, Olivier Sename and Jean-François Lafay
"Memory Resilient Gain-scheduled State-Feedback Control of Time-Delay Systems with Time-Varying Delays" (slides), 6th IFAC Symposium on Robust Control Design, Haifa, Israel, 2009
Abstract BibTeX
This paper is concerned with the stabilization of LTI/LPV time delay systems with time varying delays using LTI and LPV state-feedback controllers. First, a stability test with guaranteed input/output L2 performance is provided in terms of parameter dependent LMIs. It is obtained from a parameter dependent Lyapunov-Krasovskii functional used along with the Jensen's inequality. As the LMIs contain multiple products between system matrices and decision variables, such a result applied to synthesis problem does not lead to linearizable matrix inequalities. To overcome this problem, a relaxed version of the stability test, which leads easily to LMI synthesis conditions, is then provided. Using the relaxed result, the problem of designing both instantaneous and exact-memory state-feedback control laws is solved. The results are then extended to provide memory-resilient controller synthesis conditions. Such controllers are guaranteed to stabilize the considered system even in presence of uncertainty of the delay implemented into the controller. The interest of the approach is finally illustrated through several examples.
@inproceedings{Briat:09d,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "Memory Resilient Gain-scheduled State-Feedback Control of Time-Delay Systems with Time-Varying Delays",
year = "2009",
booktitle = "6th IFAC Symposium on Robust Control Design, Haifa, Israel, 2009"
}


27. Corentin Briat, Olivier Sename and Jean-François Lafay
"\(\mathcal{H}_\infty\) Filtering of Uncertain LPV Systems with Time-Delays" (slides), 10th European Control Conference, Budapest, Hungary, 2009
Abstract BibTeX
This paper deals with the filtering of uncertain LPV systems with time-delays. First we provide a bounded real lemma for LPV time-delay systems having a more useful structure to the filtering problem than the bounded real lemma directly obtained from the parameter dependent Lyapunov-Krasovskii functional. Using the latter result we derive sufficient conditions (in terms of parametrized LMIs) for the existence of memoryless and memory \(\mathcal{H}_\infty\) robust LPV filters. The effectiveness of the proposed approach is shown compared to existing ones in the literature.
@inproceedings{Briat:09b,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "$\mathcal{H}_\infty$ Filtering of Uncertain {LPV} Systems with Time-Delays",
year = "2009",
booktitle = "10th European Control Conference, Budapest, Hungary, 2009"
}


28. Erik Olofsson, Emmanuel Witrant, Corentin Briat, Siliviu Iulian Niculescu and Per Brunsell
"Stability Analysis and Model-Based Control in EXTRAP-T2R with Time-Delay Compensation", 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008
Abstract BibTeX
In this paper, we investigate the stability problems and control issues that occur in a reversed-field pinch (RFP) device, EXTRAP-T2R (T2R), used for research in fusion plasma physics and general plasma (ionized gas) dynamics. The plant exhibits, among other things, magnetohydrodynamic instabilities known as resistive-wall modes (RWMs), growing on a time-scale set by a surrounding non-perfectly conducting shell. We propose a novel model that takes into account experimental constraints, such as the actuators dynamics and control latencies, which lead to a multivariable time-delay model of the system. The openloop field-error characteristics are estimated and a stability analysis of the resulting closed-loop delay differential equation (DDE) emphasizes the importance of the delay effects. We then design an structurally constrained optimal PID controller by direct eigenvalue optimization (DEO) of this DDE. The presented results are substantially based on and compared with experimental data.
@inproceedings{Briat:08d,
author = "E.~Olofsson and E.~Witrant and C.~Briat and S.~I.~Niculescu and P.~Brunsell",
title = "Stability Analysis and Model-Based Control in {EXTRAP-T2R} with Time-Delay Compensation",
year = "2008",
booktitle = "47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008"
}


29. Corentin Briat and Erik I. Verriest
"A new delay-SIR Model for Pulse Vaccination", 17th IFAC World Congress, Seoul, South-Korea, July, 2008
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.
@inproceedings{Briat:08d,
author = "C.~Briat and E. I. Verriest",
title = "A New Delay-{SIR} Model for Pulse Vaccination",
year = "2008",
booktitle = "{IFAC} World Congress, Korea, Seoul"
}


30. Corentin Briat, Olivier Sename and Jean-François Lafay
"Delay-Scheduled State-Feedback Design for Time-Delay Systems with Time-Varying delays", 17th IFAC World Congress, Seoul, South-Korea, July, 2008.
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 realtime. 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 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.
@inproceedings{Briat:08a,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "Delay-Scheduled State-Feedback Design for Time-Delay Systems with Time-Varying Delays",
year = "2008",
booktitle = "{IFAC} World Congress, Korea, Seoul"
}


31. Corentin Briat, Olivier Sename and Jean-François Lafay
"Parameter dependent state-feedback control of LPV time-delay systems with time-varying delays using a projection approach", 17th IFAC World Congress, Seoul, South-Korea, July, 2008.
Abstract BibTeX
This paper is concerned with the stabilization of LPV time delay systems with time varying delays by parameter dependent state-feedback. First a stability test with H-infinity performance is given through a parameter dependent LMI. This stability test is derived from a parameter dependent Lyapunov-Krasovskii functional combined with the Jensen's inequality. From this result we derive a state-feedback existence lemma expressed through a nonlinear matrix inequality (NMI). Using a result of the paper we are able to turn this (NMI) into a bilinear matrix inequality (BMI) involving a 'slack' variable. This BMI formulation is shown to be more flexible than the initial NMI formulation and is more adequate to be solved using algorithm such as 'D-K iteration'. The controller construction is provided by two different ways. We finally discuss on the relaxation method and we show the efficiency of our method through several examples.
@inproceedings{Briat:08c,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "Parameter dependent state-feedback control of {LPV} time delay systems with time varying delays using a projection approach",
year = "2008",
booktitle = "{IFAC} World Congress, Korea, Seoul"
}


32. Corentin Briat, Olivier Sename and Jean-François Lafay
"A Full-Block \(\mathcal{S}\)-procedure application to delay-dependent \(\mathcal{H}_\infty\) state-feedback control of uncertain time-delay systems", 17th IFAC World Congress, Seoul, South-Korea, July, 2008.
Abstract BibTeX
This paper deals about the robust stabilization of uncertain systems with time-varying state delays in the delay dependent framework. The system is represented using LFR and stability is deduced from Lyapunov-Krasovskii theorem and full-block \(\mathcal{S}\)-procedure. We derive sufficient conditions to the existence of a robust \(\mathcal{H}_\infty\) state-feedback control law. As this sufficient condition is expressed in terms of nonlinear matrix inequality (NMI), we propose a relaxation based on the cone complementary algorithm which is known to lead to good results for such problems. We show the efficiency of our method trough an example.
@inproceedings{Briat:08b,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "A full-block $\mathcal{S}$-procedure application to delay-dependent ${\mathcal{H}}_\infty$ state-feedback control of uncertain time-delay systems",
year = "2008",
booktitle = "{IFAC} World Congress, Korea, Seoul"
}


33. Corentin Briat, Olivier Sename and Jean-François Lafay
"Full order LPV/\(\mathcal{H}_\infty\) observers for LPV time delay systems - a Newton Formula Approach", 3rd IFAC Symposium on System Structure and Control (SSC), Iguaçu, Brazil, 2007
Abstract BibTeX
This paper deals about the synthesis of parameter dependent observers for linear parameter varying time delay systems. These observers are computed to satisfy an \(\mathcal{H}_\infty\) performance attenuation from the disturbances to the state estimation error. First a stability test is proposed using the Lyapunov-Krasovskii approach and the Newton's formula. It is provided in terms of gridded parameter dependent LMIs. Second, this stability test is derived to obtain a sufficient condition to the existence of a (parameter dependent) observer. Our results are illustrated through an example which demonstrates the benefits of this approach.
@inproceedings{Briat:07b,
author = "C. Briat and O. Sename and J-F. Lafay",
title = "Full order {LPV}/$\mathcal{H}_\infty$ observers for {LPV} time-delay systems",
year = "2007",
booktitle = "3rd IFAC Symposium on System Structure and Control 2007, Foz do Iguacu, Brazil"
} }


34. Corentin Briat, Olivier Sename and Jean-François Lafay
"A LFT/\(\mathcal{H}_\infty\) state feedback design for Linear Parameter Varying Time Delay Systems", European Control Conference (ECC'07), Kos, Greece, July, 2007
Abstract BibTeX
This paper considers \(\mathcal{H}_\infty\) control of LPV time delay systems in LFT form. We first introduce a new model transformation for systems with time varying delay which allows us to propose a systematic method to design gain-scheduled state feedback and gain-scheduled dynamic output feedback in delay dependent framework. Further, we extend this method to elaborate a new type of controller for TDS when the delay can be measured in real time. These results are presented with single delayed systems but can be easily generalized to multiple delayed systems.
@inproceedings{Briat:07,
author = "C. Briat and O. Sename and J-F. Lafay",
title = "A {LFT}/$\mathcal{H}_\infty$ state-feedback design for Linear Parameter Varying Time delay Systems",
year = "2007",
booktitle = "European Control Conference 2007, Kos, Greece"
}


35. Olivier Sename and Corentin Briat
"\(H_\infty\) observer design for uncertain time-delay systems", European Control Conference (ECC'07), Kos, Greece, July, 2007
Abstract BibTeX
This paper is concerned with robust observer design for linear time-delay systems in the presence of unstructured uncertainties and of disturbances as well. The proposed method ensures the stability of the observer and the \(H_\infty\) attenuation of uncertainty and disturbance effects on the estimated error. The result is developed ina delay dependent framework and the observer gain matrix is obtained by solving a linear matrix inequality (LMI).
@inproceedings{Sename:07,
author = "0.~Sename and C.~Briat",
title = "Observer-based $\mathcal{H}_\infty$ control for time-delay systems: a new LMI solution",
booktitle = "European Control Conference 2007, Kos, Greece",
year = {2007},
}


36. Olivier Sename and Corentin Briat
"Observer-based \(H_\infty\) control for time-delay systems: a new LMI solution", 6th IFAC Time-Delay Systems Conference, L'Aquila, Italy, 2006
Abstract BibTeX
We propose here a new LMI solution to \(H_\infty\) observer-controller design that ensures a disturbance attenuation level for the controlled output and for the state estimation error, which is an open problem. This will be compared with a well-known solution. An application to a wind tunnel model is provided.
@inproceedings{Sename:06,
author = "O.~Sename and C.~Briat",
title = "Observer-based $\mathcal{H}_\infty$ control for time-delay systems: a new {LMI} solution",
year = "2006",
booktitle = "{IFAC} {TDS} Conference, L'Aquila, Italy",
}