A. Alessio, A. Bemporad, M. Lazar, and W. P. Heemels, Convex Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems, Proceedings of the 45th IEEE Conference on Decision and Control, pp.4532-4537, 2006.
DOI : 10.1109/CDC.2006.377495

]. B. And93 and . Anderson, Controller design : moving from theory to practice, Control Systems, vol.13, issue.4, pp.16-25, 1993.

P. [. Anta and . Tabuada, To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems, IEEE Transactions on Automatic Control, vol.55, issue.9, pp.2030-2042, 2010.
DOI : 10.1109/TAC.2010.2042980

B. [. Åström and . Wittenmark, Computer-Controlled Systems, 1997.

R. [. Böhm, F. Findeisen, and . Allgöwer, Robust control of constrained sector bounded Lur'e systems with applications to nonlinear model predictive control. Dynamics of Continuous, Discrete and Impulsive Systems, pp.935-958, 2010.

S. [. Blanchini and . Miani, Stabilization of LPV Systems: State Feedback, State Estimation, and Duality, SIAM Journal on Control and Optimization, vol.42, issue.1, pp.76-97, 2003.
DOI : 10.1137/S0363012900372283

S. [. Blanchini and . Miani, Set-Theoretic Methods in Control, Systems & Control : Foundations & Applications. Birkhäuser Basel, 2008.
DOI : 10.1007/978-3-319-17933-9

S. [. Barbot, D. Monaco, and . Normand-cyrot, A sampled normal form for feedback linearization, Mathematics of Control, Signals, and Systems, vol.7, issue.1, pp.162-188, 1996.
DOI : 10.1007/978-1-4757-2135-5_14

S. [. Castillo, S. Di-gennaro, D. Monaco, and . Normand-cyrot, On regulation under sampling. Automatic Control, IEEE Transactions on, vol.42, issue.6, pp.864-868, 1997.

B. [. Chen and . Francis, Optimal Sampled-Data Control Systems. Communications and Control Engineering, 1995.

]. C. Chi06 and . Chicon, Ordinary Differential Equations with Applications, Second Edition, 2006.

S. [. Castelan, I. Tarbouriech, and . Queinnec, Control design for a class of nonlinear continuous-time systems, Automatica, vol.44, issue.8, pp.442034-2039, 2008.
DOI : 10.1016/j.automatica.2007.11.013

[. Chen, Z. Wang, and X. Lu, On Sampled-Data Control for Master-Slave Synchronization of Chaotic Lur'e Systems, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.59, issue.8, pp.59515-519, 2012.
DOI : 10.1109/TCSII.2012.2204114

G. [. Dochain and . Bastin, Adaptive identification and control algorithms for nonlinear bacterial growth systems, Automatica, vol.20, issue.5, pp.621-634, 1984.
DOI : 10.1016/0005-1098(84)90012-8

J. [. Daafouz and . Bernussou, Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties, Systems & Control Letters, vol.43, issue.5, pp.355-359, 2001.
DOI : 10.1016/S0167-6911(01)00118-9

S. [. Duc and . Font, Commande H ? et µ-analyse : des outils pour la robustesse . Collection pédagogique d'automatique, 1999.

A. [. Deaecto and J. C. Fioravanti, Suboptimal switching control consistency analysis for discrete-time switched linear systems, European Journal of Control, vol.19, issue.3, pp.214-219, 2013.
DOI : 10.1016/j.ejcon.2013.02.008

J. [. Deaecto, J. Geromel, and . Daafouz, Dynamic output feedback H ? control of switched linear systems, Automatica, issue.8, pp.471713-1720, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00594997

L. [. De-nicolao, R. Magni, and . Scattolini, Stabilizing receding-horizon control of nonlinear time-varying systems, IEEE Transactions on Automatic Control, vol.43, issue.7, pp.1030-1036, 1998.
DOI : 10.1109/9.701133

M. [. Deaecto and J. C. Souza, State feedback switched control of discrete-time switched linear systems with application to networked control, 21st Mediterranean Conference on Control and Automation, pp.877-883, 2013.
DOI : 10.1109/MED.2013.6608825

D. [. Ebihara, D. Peaucelle, and . Arzelier, S-variable approach to LMI-Based Robust Control, Communications and Control Engineering
DOI : 10.1007/978-1-4471-6606-1

URL : https://hal.archives-ouvertes.fr/hal-01760625

M. [. Fiacchini and . Jungers, Necessary and sufficient condition for stabilizability of discrete-time linear switched systems: A set-theory approach, Automatica, vol.50, issue.1, pp.75-83, 2014.
DOI : 10.1016/j.automatica.2013.09.038

URL : https://hal.archives-ouvertes.fr/hal-00921268

Z. [. Fang, M. Lin, and . Rotea, On IQC approach to the analysis and design of linear systems subject to actuator saturation, Systems & Control Letters, vol.57, issue.8, pp.611-619, 2008.
DOI : 10.1016/j.sysconle.2007.08.016

]. E. Fri10 and . Fridman, A refined input delay approach to sampled-data control, Automatica, vol.46, pp.421-427, 2010.

E. Fridman, A. Seuret, J. C. Geromel, P. Colaneri, P. [. Bolzern et al., Dynamic output feedback control of switched linear systems Automatic Control Suboptimal switching state feedback control consistency analysis for switched linear systems Suboptimal switching control consistency analysis for switched linear systems Stabilization of sampled-data nonlinear systems by receding horizon control via discrete-time approximations Conditions for MPC Based Stabilization of Sampled-Data Nonlinear Systems Via Discrete-Time Approximations Control System Design Nonlinear oscillations, dynamical systems, and bifurcations of vector fields Applied mathematical sciences Stability analysis and stabilisation of switched nonlinear systems Stability analysis of discrete time Lur'e systems Hybrid Systems with Constraints, chapter Advanced Lyapunov functions for Lur'e systems and their switched extension Stabilization of discrete-time nonlinear systems subject to input saturations : a new Lyapunov function class, Robust sampled-data stabilization of linear systems : An input delay approach 18th IFAC World Congress 18th IFAC World Congress McInnis, and R.S. Long. Adaptive control algorithms for waste water treatment and pH neutralization. Optimal Control Applications and MethodsGrü08] L. Grüne. Input-to-state stability, numerical dynamics and sampled-data control. GAMM-Mitteilungen, pp.1441-1446720, 1982.

R. [. Goebel, A. R. Sanfelice, and . Teel, Hybrid Dynamical Systems : Modeling , Stability, and Robustness, 2012.

]. E. Gyu09 and . Gyurkovics, Sampled-data control and stability of sets for nonlinear systems, Differential Equations and Dynamical Systems, vol.17, issue.12, pp.169-183, 2009.

M. [. Hagiwara and . Araki, FR-operator approach to the H/sub 2/ analysis and synthesis of sampled-data systems, IEEE Transactions on Automatic Control, vol.40, issue.8, pp.1411-1421, 1995.
DOI : 10.1109/9.402221

C. [. Horn and . Johnson, Topics in Matrix Analysis, 1994.
DOI : 10.1017/CBO9780511840371

K. [. Heemels, P. Johansson, and . Tabuada, An introduction to eventtriggered and self-triggered control, Decision and Control (CDC), 2012 IEEE 51st Annual Conference on, pp.3270-3285, 2012.

A. [. Hetel, J. P. Kruszewski, and . Richard, A hybrid method for the analysis of non-uniformly sampled systems. in Time Delay Systems : Methods, Applications and New Trends, Series : Lecture Notes in Control and Information Sciences, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00735595

. Ti, Z. Hu, and . Lin, Composite quadratic Lyapunov functions for constrained control systems, Automatic Control IEEE Transactions on, vol.48, issue.3, pp.440-450, 2003.

S. [. Hsu and . Sastry, The effect of discretized feedback in a closed loop system, 26th IEEE Conference on Decision and Control, pp.1518-1523, 1987.
DOI : 10.1109/CDC.1987.272670

]. M. Htvn10, A. R. Heemels, N. Teel, D. Van-de-wouw, and . Ne?i´cne?i´c, Networked control systems with communication constraints : Tradeoffs between transmission intervals , delays and performance, IEEE Transactions on Automatic Control, vol.55, pp.1781-1796, 2010.

H. [. Hui, Z. Zhang, Y. Wu, and . Wang, Control synthesis problem for networked linear sampled-data control systems with band-limited channels, Information Sciences, vol.275, issue.0, pp.275385-399, 2014.
DOI : 10.1016/j.ins.2014.01.042

G. [. Iwasaki, M. Meinsma, and . Fu, -procedure and finite frequency KYP lemma, Mathematical Problems in Engineering, vol.6, issue.2-3, pp.2-3305, 2000.
DOI : 10.1155/S1024123X00001368

E. [. Jungers, S. Castelan, J. Tarbouriech, and . Daafouz, Finite -induced gain and -contractivity of discrete-time switching systems including modal nonlinearities and actuator saturations, Nonlinear Analysis: Hybrid Systems, vol.5, issue.2, pp.289-300, 2011.
DOI : 10.1016/j.nahs.2010.10.010

B. [. Jury and . Lee, On the absolute stability of nonlinear sample-data systems, IEEE Transactions on Automatic Control, vol.9, issue.4, pp.551-554, 1964.
DOI : 10.1109/TAC.1964.1105734

B. [. Keller and . Anderson, A new approach to the discretization of continuous-time controllers. Automatic Control, IEEE Transactions on, vol.37, issue.2, pp.214-223, 1992.

R. E. Kalman, LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL, Proceedings of National Academy of Sciences, pp.201-205, 1963.
DOI : 10.1073/pnas.49.2.201

]. P. Kat81 and . Katz, Digital control using microprocessors, 1981.

T. [. Kreisselmeier and . Birkholzer, Numerical nonlinear regulator design. Automatic Control, IEEE Transactions on, vol.39, issue.1, pp.33-46, 1994.
DOI : 10.1109/cdc.1992.370945

]. H. Kha02 and . Khalil, Nonlinear Systems Third Edition, 2002.

C. [. Karafyllis and . Kravaris, Global stability results for systems under sampled-data control, International Journal of Robust and Nonlinear Control, vol.34, issue.1, pp.1105-1128, 2009.
DOI : 10.1016/0167-6911(91)90135-2

M. Krsti´ckrsti´c, I. Kanellakopoulos, and P. V. Kokotovi´ckokotovi´c, Nonlinear and adaptive control design. Adaptive and learning systems for signal processing

[. Lu and D. J. Hill, Global aymptotical synchronization of chaotic Lur'e systems using sampled data : A linear matrix inequality approach, IEEE Transactions on Circuits and Systems II : Express Briefs, vol.55, issue.6, pp.586-590, 2008.

W. [. Li, B. Heath, and . Lennox, An improved stability criterion for a class of lur'e systems, IEEE Conference on Decision and Control, pp.4483-4488, 2007.

W. [. Li, B. Heath, and . Lennox, Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program, Control Theory Applications, IET, pp.554-563, 2008.
DOI : 10.1049/iet-cta:20070225

]. J. Ljd13a, M. Louis, J. Jungers, and . Daafouz, On using disconnected level sets Lyapunov functions in the context of sampled-data systems, 52nd IEEE Conference on Decision and Control, CDC 2013, pp.630-635, 2013.

]. J. Ljd13b, M. Louis, J. Jungers, and . Daafouz, Sur l'utilisation d'une fonction de Lyapunov à lignes de niveau non-connexes, Journal Européen des Systèmes Automatisés, vol.47, pp.4-8483, 2013.

]. J. Ljd15a, M. Louis, J. Jungers, and . Daafouz, Consistance des systèmes de Lurée commutées : application à la synthèse de commande numérique avec échantillonnage non uniforme, 6e Journées Doctorales / Journées Nationales MACS, JD-JN-MACS 2013, p.page CDROM, 2015.

]. J. Ljd15b, M. Louis, J. Jungers, and . Daafouz, Stabilization of sampled-data Lur'e systems with nonuniform sampling, 54th IEEE Conference on Decision and Control, 2015.

]. J. Ljd15c, M. Louis, J. Jungers, and . Daafouz, Sufficient LMI stability conditions for Lur'e type systems governed by a control law designed on their Euler approximate model, International Journal of Control, vol.88, issue.9, pp.1841-1850, 2015.

]. J. Ljd15d, M. Louis, J. Jungers, and . Daafouz, Switching control consistency of switched Lur'e systems with application to digital control design with non uniform sampling, 14th annual European Control Conference, 2015.

D. [. Laila, A. Ne?i´cne?i´c, and . Astolfi, Advanced topics in control systems theory II, volume 328 of Lecture notes from FAP 2006, chapter Sampled-Data Control of Nonlinear Systems, pp.91-137, 2005.

D. [. Laila, A. R. Ne?i´cne?i´c, and . Teel, Open- and Closed-Loop Dissipation Inequalities Under Sampling and Controller Emulation, European Journal of Control, vol.8, issue.2, pp.109-125, 2002.
DOI : 10.3166/ejc.8.109-125

]. J. Lou13 and . Louis, Discrétisation et analyse de stabilité des systèmes de type Lur'e, 5e Journées Doctorales / Journées Nationales MACS, JD-JN-MACS 2013, p.page CDROM, 2013.

V. [. Lur-'e and . Postnikov, On the theory of stability of control systems, Applied Mathematics and Mechanics, vol.8, issue.3, pp.3-13, 1944.

L. [. Matsumoto, M. Chua, and . Komuro, The double scroll. Circuits and Systems, IEEE Transactions on, vol.32, issue.8, pp.797-818, 1985.

D. [. Monaco and . Normand-cyrot, On the sampling of a linear analytic control system, 1985 24th IEEE Conference on Decision and Control, pp.1457-1462, 1985.
DOI : 10.1109/CDC.1985.268753

A. [. Megretski, M. Rantzer, L. Moarref, and . Rodrigues, System analysis via integral quadratic constraints, IEEE Transactions on Automatic Control, vol.42, issue.6, pp.819-830, 1997.
DOI : 10.1109/9.587335

L. [. Ne?i´cne?i´c and . Grüne, Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation, Automatica, vol.41, issue.7, pp.1143-1156, 2005.
DOI : 10.1016/j.automatica.2005.03.001

A. [. Ne?i´cne?i´c and . Teel, A Framework for Stabilization of Nonlinear Sampled-Data Systems Based on Their Approximate Discrete-Time Models, IEEE Transactions on Automatic Control, vol.49, issue.7, pp.1103-1122, 2004.
DOI : 10.1109/TAC.2004.831175

A. [. Ne?i´cne?i´c and . Teel, Stabilization of sampled-data nonlinear systems via backstepping on their euler approximate model, Automatica, issue.10, pp.421801-1808, 2006.

A. [. Ne?i´cne?i´c, D. Teel, and . Carnevale, Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems, IEEE Transactions on Automatic Control, vol.54, issue.3, pp.619-624, 2009.
DOI : 10.1109/TAC.2008.2009597

D. Ne?i´cne?i´c, A. R. Teel, and P. V. Kokotovi´ckokotovi´c, On the design of a controller based on the discrete-time approximation of the nonlinear plant model, American Control Conference Proceedings of the 1999, pp.3474-3478, 1999.

D. Ne?i´cne?i´c, A. R. Teel, P. V. Kokotovi´ckokotovi´c, D. Ne?i´cne?i´c, A. R. Teel et al., Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems On the Lyapunov-based adaptative control redesign for a class of nonlinear sampleddata systems [Pet87] I.R. Petersen. A stabilization algorithm for a class of uncertain linear systems On the asymptotic stability of a class of saturating sampled-data systems Discrete-time Positive-Real lemma revisited : the discrete-time counterpart Kalman-Yakubovich lemma Absolute stability of nonlinear systems of automatic control A method for parameter estimation in Lur'e systems The analysis of optimization based controllers Padé discretization for linear systems with polyhedral Lyapunov functions A full block S-procedure with applications, Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations. Systems & Control LettersPoz10] A. Poznyak. Advanced Mathematical Tools for Control Engineers Deterministic Systems. Advanced Mathematical Tools for Automatic Control Engineers Decision and Control Proceedings of the 36th IEEE Conference onSCSS11] R. Shorten, M. Corless, S. Sajja, and S. Solmaz. On Padé approximations, quadratic stability and discretization of switched linear systemsSDGD14] M. Souza, G.S. Deaecto, J.C. Geromel, and J. Daafouz. Self-triggered linear quadratic networked control. Optimal Control Applications and Methods, pp.259-27049, 1961.

]. A. Seu12 and . Seuret, A novel stability analysis of linear systems under asynchronous samplings, Automatica, vol.48, issue.1, pp.177-182, 2012.

]. S. Str94 and . Strogatz, Nonlinear Dynamics and Chaos : With Applications to Physics , Biology, Chemistry, and Engineering. Advanced book program, 1994.

]. Y. Suh08 and . Suh, Stability and stabilization of nonuniform sampling systems, Automatica, vol.44, issue.12, pp.3222-3226, 2008.
DOI : 10.1016/j.automatica.2008.10.002

]. G. Sze63 and . Szegö, On the absolute stability of sampled-data control systems, Proceedings of National Academy of Sciences, vol.50, pp.558-560, 1963.

P. [. Theesar and . Balasubramaniam, Secure Communication via Synchronization of Lur???e Systems Using Sampled-Data Controller, Circuits, Systems, and Signal Processing, vol.56, issue.4, pp.37-52, 2014.
DOI : 10.1109/TCSII.2009.2015388

M. [. Turner, I. Kerr, and . Postlethwaite, On the existence of stable, causal multipliers for systems with slope-restricted nonlinearities, American Control Conference ACC '09, pp.121-126, 2009.

]. S. Tpds06, C. Tarbouriech, J. M. Prieur, and . Da-silva, Stability analysis and stabilization of systems presenting nested saturations. Automatic Control, IEEE Transactions on, issue.8, pp.511364-1371, 2006.

]. Y. Tsy62 and . Tsypkin, The absolute stability of large-scale nonlinear sampled-data systems, Doklady Akademii Nauk SSSR, vol.145, pp.52-55, 1962.

. M. Vfm03, J. M. Velasco, P. Fuertes, and . Marti, The self triggered task model for realtime control systems, 24th IEEE Real-Time Systems Symposium (work in progress, pp.67-70, 2003.

M. [. Wang and . Lemmon, Self-triggering under state-independent disturbances . Automatic Control, IEEE Transactions on, vol.55, issue.6, pp.1494-1500, 2010.

]. V. Yak62 and . Yakubovich, Solution of some matrix inequalities encountered in the automatic control theory, Doklady Akademii Nak, vol.43, pp.1304-1307, 1962.

[. Zhang, Y. He, and M. Wu, Improved Global Asymptotical Synchronization of Chaotic Lur'e Systems With Sampled-Data Control, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.56, issue.4, pp.320-324, 2009.
DOI : 10.1109/TCSII.2009.2015388

W. De-lorraine-le-président-de-l-'université-de-lorraine-autorise, M. Julien, L. Louis, and . Vu, Sur proposition de M. Jamal DAAFOUZ, directeur de thèse, à soutenir la thèse de doctorat, préparée sous la direction de M, arrêté du 07 août 2006 relatif à la formation doctorale Jamal DAAFOUZ, intitulée Discrétisation des systèmes de Lur ' e : stabilisation et consistance La soutenance aura lieu le 27 août 2015 à 1Oh30 Université de Lorraine-Site de Brabois