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 closedloop 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 = "1140511410",
}



2.  Corentin Briat and Mustafa Khammash 
 "Simple interval observers for linear impulsive systems with applications to sampleddata 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 dwelltime constraints are obtained and formulated in terms of infinitedimensional 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 infinitedimensional 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 dwelltime constraint, the second one is about the interval observation of an aperiodic sampleddata 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 sampleddata and switched systems",
booktitle="20th IFAC World Congress",
year= "2017",
address = "Toulouse, France",
pages = "52355240",
}



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 ParameterVarying (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 wellknown quadratic and robust stability criteria together. The obtained conditions being infinitedimensional, a relaxation approach based on sum of squares programming is used in order to obtain tractable finitedimensional 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 = "78157820",
}



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 socalled 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 = "752757",
}



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
Closedloop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the openloop systems which implies feedback wellposedness 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 timevarying and nonlinear feedback systems is studied using ILC, paralleling the wellknown 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 = "63736378",
}



6.  Igor Pontes Duff, Pierre Vuillemin, Charles PoussotVassal, Corentin Briat and Cédric Seren 
 "Approximation of stability regions for largescale timedelay 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 largescale timedelay systems
(LS TDS) is solved using model approximation techniques. To
achieve this, an \(\mathcal{H}_2\) oriented approximation algorithm, referred
to as TFIRKA, is considered. This algorithm has been
shown to be well suited for the approximation of infinite
dimensional systems into finitedimensional 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. {PoussotVassal} and C. Briat and C. Seren",
title= "Approximation of stability regions for largescale timedelay 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 PoussotVassal, Cédric Seren and Corentin Briat 
 "Stability and performance analysis of largescale aircraft vibration delay model using model reduction techniques", EuroGNC, Toulouse, France, 2015 

Abstract
BibTeX
In this paper, the problem estimate stability and computing the frequencylimited \(\mathcal{H}_{2,\Omega}\) performances of an antivibration controller subject to feedback time
delays is considered. The contribution of this paper lies in the application of realizationless model reduction techniques on a largescale 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. {PoussotVassal} and C. Seren and C. Briat",
title= "Stability and performance analysis of largescale 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 sampleddata systems with discretetime constant input delay" (slides), 53rd IEEE Conference on Decision and Control, Los Angeles, USA, 2014 

Abstract
BibTeX
Aperiodic sampleddata systems controlled by a delayed statefeedback controller arise naturally in networked control systems. We propose a novel way to analyze the stability of sampleddata systems with discretetime constant input delay by, first, reformulating the system into an aperiodic discretetime system with constant delay and by, then, considering a mixture of a discretetime LyapunovKrasovskii functional and a loopedfunctional 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 (timevarying) systems. An example is given for illustration.
@inproceedings{Briat:14cdc,
author= "A. Seuret and C. Briat and F. Gouaisbaut",
title= "Stability analysis of asynchronous sampleddata systems with discretetime constant input delay",
booktitle="53rd IEEE Conference on Decision and Control",
year= "2014",
address = "Los Angeles, USA",
pages = "43424347",
}



10.  Corentin Briat, Ankit Gupta, Iman Shames and Mustafa Khammash 
 "Scalable tests for ergodicity analysis of largescale 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 largescale interconnected stochastic reaction networks",
booktitle="21st International Symposium on Mathematical Theory of Networks and Systems",
year= "2014",
address = "Groningen, The Netherlands",
pages = "9295",
}



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 upperbound 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 = "33673372",
}



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 = "35823588",
}



13.  Corentin Briat and Alexandre Seuret 
 "Robust stability of impulsive systems: A functionalbased approach" (slides), 4th IFAC Conference on analysis and design of hybrid systems (ADHS'12), Eindhoven, the Netherlands, 2012. 

Abstract
BibTeX
An improved functionalbased approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov loopedfunctionals is provided. Looped functionals are particular functionals that allow to encode discretetime stability criteria into continuoustime conditions and to consider nonmonotonic Lyapunov functions along the trajectories of the impulsive system. Unlike usual discretetime 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 functionalbased approach",
booktitle="4th IFAC Conference on analysis and design of hybrid systems (ADHS'12), Eindhoven, the Netherlands, 2012",
year= "2012",
pages = "412417",
}



14.  Burak Demirel, Corentin Briat and Mikael Johansson 
 "Supervisory Control Design for Networked Systems with TimeVarying 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
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 analysis
conditions that can be verified by semidefinite programming, and show that associated state
feedback synthesis problem also can be solved using convex optimization. A widearea 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 TimeVarying Communication Delays",
booktitle="4th IFAC Conference on analysis and design of hybrid systems (ADHS'12), Eindhoven, the Netherlands, 2012",
year= "2012",
pages = "133140",
}



15.  Corentin Briat, Emre Altug Yavuz and Gunnar Karlsson 
 "A conservationlawbased modular fluidflow model for network congestion modeling" (slides), 31st IEEE International Conference on Computer Communications (INFOCOM'12), Orlando, Florida, USA, 2012 

Abstract
BibTeX
A modular fluidflow 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 packetlevel simulations corroborate the proposed model.
@inproceedings{Briat:12infocom,
author= "C. Briat and E. A. Yavuz and G. Karlsson",
title= "A conservationlawbased modular fluidflow model for network congestion modeling",
booktitle="31st {IEEE} International Conference on Computer Communications (INFOCOM'12), Orlando, Florida, USA",
year= "2012",
pages = "20502058",
}



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 supplyrates 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 inputoutput 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 staticgain of the uncertainties, only, is critical for stability. This fact provides a new explanation for the surprising stability properties of linear positive timedelay 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 = "31223129",
}



17.  Corentin Briat 
 "Robust stability analysis in the *norm and LyapunovRazumikhin functions for the stability analysis and control of timedelay systems" (slides), 50th IEEE Conference on Decision and Control, Orlando, Florida, USA, 2011 

Abstract
BibTeX
LyapunovKrasovskii functionals have been shown to have connections with inputoutput techniques considering delay operators mapping \(L_2\) to \(L_2\). It is shown here that LyapunovRazumikhin functions can also be connected to the inputoutput framework by considering operators on \(L_\infty\). Several important results from the LyapunovRazumikhin Theorem are retrieved and extended.
@inproceedings{Briat:11cdc2,
author= "Corentin~Briat",
title= "Robust stability analysis in the $*$norm and LyapunovRazumikhin functions for the stability analysis and control of timedelay systems",
booktitle="50th IEEE Conference on Decision and Control, Orlando, USA",
year= "2011",
pages = "63196324",
}



18.  Corentin Briat, Håkan Hjalmarsson, Gunnar Karlsson, Karl Henrik Johansson, Ulf T. Jönsson, Henrik Sandberg and Emre Altug Yavuz 
 "An axiomatic fluidflow 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 singlebuffer/multipleusers 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 fluidflow model for congestion control analysis",
booktitle="50th IEEE Conference on Decision and Control, Orlando, USA",
year= "2011",
pages = "31223129",
}



19.  Yassine Ariba, Corentin Briat and Karl Henrik Johansson 
 "Simple conditions for L_{2} 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 timevarying 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 = "96101",
}



20.  Corentin Briat and Ulf T. Jönsson 
 "Dynamic equations on timescale: application to stability analysis and stabilization of aperiodic sampleddata 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 timescales. Lyapunov theory is used, with sampleperioddependent 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 statefeedback are provided; both robust and samplingperioddependent 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 timescale: application to stability analysis and stabilization of aperiodic sampleddata systems",
year = "2011",
booktitle = "18th IFAC World Congress, Milano, Italy, 2011",
pages = "1137411379",
}



21.  Corentin Briat and Alexandre Seuret 
 "Stability Criteria for Asynchronous Sampleddata Systems  A Fragmentation Approach" (slides), 18th IFAC World Congress, Milano, Italy, 2011. 

Abstract
BibTeX
The stability analysis of asynchronous sampleddata systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampleddata systems in a continuoustime 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 timedelay 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 Sampleddata Systems  A Fragmentation Approach",
year = "2011",
booktitle = "18th IFAC World Congress, Milano, Italy, 2011",
pages = "13131318",
}



22.  Corentin Briat and John Jairo MartinezMolina 
 "\(\mathcal{H}_\infty\) Bounded Resilient statefeedback design for linear continuoustime systems  A robust control approach" (slides), 18th IFAC World Congress, Milano, Italy, 2011. 

Abstract
BibTeX
The quadratic stabilization of LTI systems by bounded resilient statefeedback controllers is addressed. The controllers are guaranteed to be nonfragile 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 NPHard 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 statefeedback design for linear continuoustime systems  A robust control approach",
year = "2011",
booktitle = "18th IFAC World Congress, Milano, Italy, 2011",
pages = "93079312",
}



23.  Corentin Briat, Emre Altug Yavuz and Gunnar Karlsson 
 "Impact of propagation delay estimation error on equilibrium and its stability" (slides), 10th International IFIPTC6 Networking Conference, Valencia, Spain, 2011 

Abstract
BibTeX
Delaybased transmission control protocols need to separate roundtrip 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 FASTTCP as a representative delaybased 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 IFIPTC6 Networking Conference, Valencia, Spain",
year= "2011",
pages = "356367",
}



24.  Corentin Briat, Håkan Hjalmarsson, Gunnar Karlsson, Karl Henrik Johansson, Ulf T. Jönsson and Henrik Sandberg 
 "Nonlinear statedependent 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 closedloop is statedependent 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 delayderivative 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 delayfree single buffer network. Finally, using a specific linearization result for systems with statedependent 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 statedependent 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 MartinezMolina 
 "Design of \(\mathcal{H}_\infty\) Bounded NonFragile Controllers for DiscreteTime Systems" (slides), 48th IEEE Conference on Decision and Control, Shanghai, China, 2009 

Abstract
BibTeX
This paper deals with the quadratic stabilization of discretetime LTI systems using statefeedback controllers with bounded coefficients. The controllers are guaranteed to be nonfragile with respect to additive or multiplicative implementation errors. The approach is based on robustcontrol 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 NonFragile Controllers for DiscreteTime Systems",
year = "2009",
booktitle = "48th Conference on Decision and Control, Shanghai, China, 2009"
}



26.  Corentin Briat, Olivier Sename and JeanFrançois Lafay 
 "Memory Resilient Gainscheduled StateFeedback Control of TimeDelay Systems with TimeVarying 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 statefeedback 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 LyapunovKrasovskii 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 exactmemory statefeedback control laws is solved. The results are then extended to provide memoryresilient 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 Gainscheduled StateFeedback Control of TimeDelay Systems with TimeVarying Delays",
year = "2009",
booktitle = "6th IFAC Symposium on Robust Control Design, Haifa, Israel, 2009"
}



27.  Corentin Briat, Olivier Sename and JeanFrançois Lafay 
 "\(\mathcal{H}_\infty\) Filtering of Uncertain LPV Systems with TimeDelays" (slides), 10th European Control Conference, Budapest, Hungary, 2009 

Abstract
BibTeX
This paper deals with the filtering of uncertain LPV systems with timedelays. First we provide a bounded real lemma for LPV timedelay systems having a more useful structure to the filtering problem than the bounded real lemma directly obtained from the parameter dependent LyapunovKrasovskii 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 TimeDelays",
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 ModelBased Control in EXTRAPT2R with TimeDelay 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 reversedfield pinch (RFP) device, EXTRAPT2R (T2R), used for research in fusion plasma physics and general plasma (ionized gas) dynamics. The plant exhibits, among other things, magnetohydrodynamic instabilities known as resistivewall modes (RWMs), growing on a timescale set by a surrounding nonperfectly 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 timedelay model of the system. The openloop fielderror characteristics are estimated and a stability analysis of the resulting closedloop 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 ModelBased Control in {EXTRAPT2R} with TimeDelay Compensation",
year = "2008",
booktitle = "47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008"
}



29.  Corentin Briat and Erik I. Verriest 
 "A new delaySIR Model for Pulse Vaccination", 17th IFAC World Congress, Seoul, SouthKorea, 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 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.
@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 JeanFrançois Lafay 
 "DelayScheduled StateFeedback Design for TimeDelay Systems with TimeVarying delays", 17th IFAC World Congress, Seoul, SouthKorea, July, 2008. 

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 full block Sprocedure 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.
@inproceedings{Briat:08a,
author = "C.~Briat and O.~Sename and J.F.~Lafay",
title = "DelayScheduled StateFeedback Design for TimeDelay Systems with TimeVarying Delays",
year = "2008",
booktitle = "{IFAC} World Congress, Korea, Seoul"
}



31.  Corentin Briat, Olivier Sename and JeanFrançois Lafay 
 "Parameter dependent statefeedback control of LPV timedelay systems with timevarying delays using a projection approach", 17th IFAC World Congress, Seoul, SouthKorea, July, 2008. 

Abstract
BibTeX
This paper is concerned with the stabilization of LPV time delay systems with time varying delays by parameter dependent statefeedback. First a stability test with Hinfinity performance is given through a parameter dependent LMI. This stability test is derived from a parameter dependent LyapunovKrasovskii functional combined with the Jensen's inequality. From this result we derive a statefeedback 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 'DK 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 statefeedback 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 JeanFrançois Lafay 
 "A FullBlock \(\mathcal{S}\)procedure application to delaydependent \(\mathcal{H}_\infty\) statefeedback control of uncertain timedelay systems", 17th IFAC World Congress, Seoul, SouthKorea, July, 2008. 

Abstract
BibTeX
This paper deals about the robust stabilization of uncertain systems with timevarying state delays in the delay dependent framework. The system is represented using LFR and stability is deduced from LyapunovKrasovskii theorem and fullblock \(\mathcal{S}\)procedure. We derive sufficient conditions to the existence of a robust \(\mathcal{H}_\infty\) statefeedback 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 fullblock $\mathcal{S}$procedure application to delaydependent ${\mathcal{H}}_\infty$ statefeedback control of uncertain timedelay systems",
year = "2008",
booktitle = "{IFAC} World Congress, Korea, Seoul"
}



33.  Corentin Briat, Olivier Sename and JeanFrançois 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 LyapunovKrasovskii 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 JF. Lafay",
title = "Full order {LPV}/$\mathcal{H}_\infty$ observers for {LPV} timedelay systems",
year = "2007",
booktitle = "3rd IFAC Symposium on System Structure and Control 2007, Foz do Iguacu, Brazil"
} }



34.  Corentin Briat, Olivier Sename and JeanFrançois 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 gainscheduled state feedback and gainscheduled 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 JF. Lafay",
title = "A {LFT}/$\mathcal{H}_\infty$ statefeedback 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 timedelay systems", European Control Conference (ECC'07), Kos, Greece, July, 2007 

Abstract
BibTeX
This paper is concerned with robust observer design for linear timedelay 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 = "Observerbased $\mathcal{H}_\infty$ control for timedelay systems: a new LMI solution",
booktitle = "European Control Conference 2007, Kos, Greece",
year = {2007},
}



36.  Olivier Sename and Corentin Briat 
 "Observerbased \(H_\infty\) control for timedelay systems: a new LMI solution", 6th IFAC TimeDelay Systems Conference, L'Aquila, Italy, 2006 

Abstract
BibTeX
We propose here a new LMI solution to \(H_\infty\) observercontroller 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 wellknown solution. An application to a wind tunnel model is provided.
@inproceedings{Sename:06,
author = "O.~Sename and C.~Briat",
title = "Observerbased $\mathcal{H}_\infty$ control for timedelay systems: a new {LMI} solution",
year = "2006",
booktitle = "{IFAC} {TDS} Conference, L'Aquila, Italy",
}


