T. Bibliography, . Alamo, E. Bravo, and . Camacho, Guaranteed state estimation by zonotopes, Automatica, vol.41, issue.6, pp.1035-1043, 2005.

A. Alessio, M. Lazar, A. Bemporad, and W. Heemels, Squaring the circle: An algorithm for generating polyhedral invariant sets from ellipsoidal ones, Automatica, vol.43, issue.12, pp.43-2096, 2007.
DOI : 10.1016/j.automatica.2007.04.028

F. Ancona and A. Bressan, Stabilization by patchy feedbacks and robustness properties. Optimal control, stabilization and nonsmooth analysis, pp.185-199, 2004.

B. D. Anderson and J. B. Moore, Optimal control: linear quadratic methods, NJ, 1989.

Z. Artstein and S. V. Rakovi´crakovi´c, Feedback and invariance under uncertainty via set-iterates, Automatica, vol.44, issue.2, pp.520-525, 2008.
DOI : 10.1016/j.automatica.2007.06.013

E. Asarin, O. Bournez, T. Dang, and O. Maler, Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems, Hybrid Systems: Computation and Control, pp.20-31, 2000.
DOI : 10.1007/3-540-46430-1_6
URL : https://hal.archives-ouvertes.fr/inria-00099316

J. Pierre-aubin, Viability theory, 1991.
URL : https://hal.archives-ouvertes.fr/inria-00636570

J. Pierre-aubin and H. Frankowska, Set-valued analysis, 2008.

D. Avis and K. Fukuda, Reverse search for enumeration, Discrete Applied Mathematics, vol.65, issue.1-3, pp.21-46, 1996.
DOI : 10.1016/0166-218X(95)00026-N

A. Bemporad and M. Morari, Control of systems integrating logic, dynamics, and constraints, Automatica, vol.35, issue.3, pp.407-428, 1999.
DOI : 10.1016/S0005-1098(98)00178-2

D. P. Bertsekas, D. P. Bertsekas, D. P. Bertsekas, and D. P. Bertsekas, Dynamic programming and optimal control, 1995.

R. R. Bitmead, M. Gevers, and V. Wertz, Adaptive Optimal Control: The Thinking Man\'s {G}{P}{C}, 1990.

G. Bitsoris, On the positive invariance of polyhedral sets for discrete-time systems, Systems & Control Letters, vol.11, issue.3, pp.243-248, 1988.
DOI : 10.1016/0167-6911(88)90065-5

G. Bitsoris and M. Vassilaki, Design Techniques of Linear Constrained Discrete-Time Control Systems, Control and Dynamic Systems, vol.56, pp.1-49, 1993.
DOI : 10.1016/B978-0-12-012756-6.50007-4

F. Blanchini, Nonquadratic Lyapunov functions for robust control, Automatica, vol.31, issue.3, pp.31-451, 1995.
DOI : 10.1016/0005-1098(94)00133-4

F. Blanchini, Set invariance in control, Automatica, vol.35, issue.11, pp.1747-1767, 1999.
DOI : 10.1016/S0005-1098(99)00113-2

F. Blanchini and S. Miani, Set-theoretic methods in control, 2007.
DOI : 10.1007/978-3-319-17933-9

M. Blanke, Consistent design of dependable control systems, Control Engineering Practice, vol.4, issue.9, pp.1305-1312, 1996.
DOI : 10.1016/0967-0661(96)00138-4

M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki, Diagnosis and fault-tolerant control, 2006.

O. N. Bobyleva and E. S. Pyatnitskii, Piecewise-linear Lyapunov functions and localization of spectra of stable matrices. Automation and Remote Control, pp.1417-1427, 2001.

J. Bourgain and J. Lindenstrauss, Distribution of points on spheres and approximation by zonotopes, Israel Journal of Mathematics, vol.129, issue.1, pp.25-31, 1988.
DOI : 10.1007/BF02767366

M. S. Branicky, Stability of switched and hybrid systems, Proceedings of 1994 33rd IEEE Conference on Decision and Control, pp.3498-3498, 1994.
DOI : 10.1109/CDC.1994.411688

R. Brayton and C. Tong, Stability of dynamical systems: A constructive approach. Circuits and Systems, IEEE Transactions on, vol.26, issue.4, pp.224-234, 1979.

E. Bronstein, Approximation of convex sets by polytopes, Journal of Mathematical Sciences, vol.31, issue.5, pp.727-762, 2008.
DOI : 10.1007/s10958-008-9144-x

R. Buck, Partition of Space, The American Mathematical Monthly, vol.50, issue.9, pp.541-544, 1943.
DOI : 10.2307/2303424

M. B. Cloosterman, N. Van-de-wouw, W. M. Heemels, and H. Nijmeijer, Robust Stability of Networked Control Systems with Time-varying Network-induced Delays, Proceedings of the 45th IEEE Conference on Decision and Control, pp.4980-4985, 2006.
DOI : 10.1109/CDC.2006.376765

E. Crück, Target problems under state constraints for anisotropic affine dynamics: A numerical analysis based on viability theory, Proc. of the 17th IFAC World Congress, pp.14354-14359, 2008.

T. Dang, Approximate reachability computation for polynomial systems Hybrid Systems: Computation and Control, pp.138-152, 2006.

G. B. Dantzig, Fourier-Motzkin elimination and its dual, Journal of Combinatorial Theory, Series A, vol.14, issue.3, 1972.
DOI : 10.1016/0097-3165(73)90004-6
URL : http://doi.org/10.1016/0097-3165(73)90004-6

C. Dórea and J. C. Hennet, On (a, b)-invariance of polyhedral domains for discretetime systems, Decision and Control Proceedings of the 35th IEEE, pp.4319-4324, 1996.

M. G. Earl and R. , Modeling and control of a multi-agent system using mixed integer linear programming, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., pp.107-111, 2001.
DOI : 10.1109/CDC.2002.1184476

W. Elmenreich and S. Pitzek, The time-triggered sensor fusion model, Proceedings of the 5th IEEE International Conference on Intelligent Engineering Systems, pp.297-300, 2001.

J. A. Ferrez and K. Fukuda, Implementations of lp-based reverse search algorithms for the zonotope construction and the xed-rank convex quadratic maximization in binary variables using the zram and the cddlib libraries, 2002.

H. Frankowska, Lower semicontinuous solutions to hamilton-jacobi-bellman equations, Decision and Control Proceedings of the 30th IEEE Conference on, pp.265-270, 1991.
DOI : 10.1109/cdc.1991.261303

K. Fukuda, Polytope examples. URL http

K. Fukuda, cdd/cdd+ reference manual. Institute for operations Research ETH- Zentrum, 1999.

K. Fukuda, From the zonotope construction to the Minkowski addition of convex polytopes, Journal of Symbolic Computation, vol.38, issue.4, pp.1261-1272, 2004.
DOI : 10.1016/j.jsc.2003.08.007

M. R. Garey and D. S. Johnson, Computers and intractability. A guide to the theory of NP-completeness. A Series of Books in the Mathematical Sciences, WH Freeman and Company, 1979.

J. Geromel and P. Colaneri, Stability and stabilization of discrete time switched systems, International Journal of Control, vol.280, issue.7, pp.719-728, 2006.
DOI : 10.1109/9.664149

T. Geyer, F. D. Torrisi, and M. Morari, Optimal complexity reduction of piecewise affine models based on hyperplane arrangements, Proceedings of the 23th American Control Conference, pp.1190-1195, 2004.

T. Geyer, F. D. Torrisi, and M. Morari, Optimal complexity reduction of polyhedral piecewise affine systems, Automatica, vol.44, issue.7, pp.1728-1740, 2008.
DOI : 10.1016/j.automatica.2007.11.027

R. Gielen, M. Lazar, and S. Olaru, Set-Induced Stability Results for Delay Difference Equations, Control and Information Sciences, 2011.
DOI : 10.1007/978-3-642-25221-1_6
URL : https://hal.archives-ouvertes.fr/hal-00750901

E. Gilbert and K. Tan, Linear systems with state and control constraints: the theory and application of maximal output admissible sets, IEEE Transactions on Automatic Control, vol.36, issue.9, pp.1008-1020, 1991.
DOI : 10.1109/9.83532

P. J. Goulart, E. C. Kerrigan, and J. M. Maciejowski, Optimization over state feedback policies for robust control with constraints, Automatica, vol.42, issue.4, pp.523-533, 2006.
DOI : 10.1016/j.automatica.2005.08.023

P. Gritzmann and V. Klee, On the complexity of some basic problems in computational convexity: I. Containment problems, Discrete Mathematics, vol.136, issue.1-3, pp.129-174, 1994.
DOI : 10.1016/0012-365X(94)00111-U

P. Gritzmann and V. Klee, On the Complexity of Some Basic Problems in Computational Convexity, NATO ASI Series C Mathematical and Physical Sciences-Advanced Study Institute, pp.373-466, 1994.
DOI : 10.1007/978-94-011-0924-6_17

H. Haimovich and M. Seron, Componentwise ultimate bound and invariant set computation for switched linear systems, Automatica, vol.46, issue.11, 2010.
DOI : 10.1016/j.automatica.2010.08.018
URL : http://ogma.newcastle.edu.au:8080/vital/access/manager/Repository/uon:9795/ATTACHMENT01

H. Haimovich, E. Kofman, M. M. Seron, I. Agrimensura, and R. De-rosario, Analysis and Improvements of a Systematic Componentwise Ultimatebound Computation Method, Proccedings of the 17th World Congress IFAC, 2008.

K. Hamiti, A. Voda-besancon, and H. Roux-buisson, Position control of a pneumatic actuator under the influence of stiction, Control Engineering Practice, vol.4, issue.8, pp.1079-1088, 1996.
DOI : 10.1016/0967-0661(96)00106-2

J. W. Helton and V. Vinnikov, Linear matrix inequality representation of sets, Communications on Pure and Applied Mathematics, vol.289, issue.5, pp.654-674, 2007.
DOI : 10.1002/cpa.20155

D. Henrion, Semidefinite Representation of Convex Hulls of Rational Varieties, Acta Applicandae Mathematicae, vol.26, issue.1, 2009.
DOI : 10.1007/s10440-011-9623-9
URL : https://hal.archives-ouvertes.fr/hal-00352788

D. Henrion and A. Garulli, Positive polynomials in control, 2005.
DOI : 10.1007/b96977

D. Henrion and J. B. Lasserre, Convergent relaxations of polynomial matrix inequalities and static output feedback. Automatic Control, IEEE Transactions on, vol.51, issue.2, pp.192-202, 2006.

H. Hindi, A tutorial on convex optimization, Proceedings of the 23th American Control Conference, pp.3252-3265, 2004.

C. S. Hsieh, Performance gain margins of the two-stage LQ reliable control, Automatica, vol.38, issue.11, pp.1985-1990, 2002.
DOI : 10.1016/S0005-1098(02)00114-0

A. Ingimundarson, J. M. Bravo, V. Puig, T. Alamo, and P. Guerra, Robust fault detection using zonotope-based set-membership consistency test, International Journal of Adaptive Control and Signal Processing, vol.12, issue.1, pp.311-330, 2009.
DOI : 10.1002/acs.1038

R. Isermann, Supervision, fault-detection and fault-diagnosis methods ??? An introduction, Control Engineering Practice, vol.5, issue.5, pp.639-652, 1997.
DOI : 10.1016/S0967-0661(97)00046-4

J. Jiang, Why does one need fault-tolerant control systems anyway?, 2010 Conference on Control and Fault-Tolerant Systems (SysTol), pp.118-118, 2010.
DOI : 10.1109/SYSTOL.2010.5675943

J. Jiang and Q. Zhao, Design of Reliable Control Systems Possessing Actuator Redundancies, Journal of Guidance, Control, and Dynamics, vol.23, issue.4, pp.709-718, 2000.
DOI : 10.2514/2.4587

C. N. Jones, E. C. Kerrigan, and J. M. Maciejowski, Equality set projection: A new algorithm for the projection of polytopes in halfspace representation, Citeseer, 2004.

E. C. Kerrigan and J. M. Maciejowski, Feedback min-max model predictive control using a single linear program: robust stability and the explicit solution, International Journal of Robust and Nonlinear Control, vol.14, issue.4, pp.395-413, 2004.
DOI : 10.1002/rnc.889

U. Kiencke and L. Nielsen, Automotive control systems: for engine, driveline, and vehicle, Measurement Science and Technology, vol.11, p.1828, 2000.

H. Kiendl, J. Adamy, and P. Stelzner, Vector norms as Lyapunov functions for linear systems, IEEE Transactions on Automatic Control, vol.37, issue.6, pp.839-842, 1992.
DOI : 10.1109/9.256362

D. Kim and Y. Kim, Robust variable structure controller design for fault tolerant flight control, AIAA Guidance, Navigation, and Control Conference and Exhibit, pp.750-759, 1998.

K. Kobayashi and J. Imura, Modeling of discrete dynamics for computational time reduction of Model Predictive Control, Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, pp.628-633, 2006.

E. Kofman, Non-conservative ultimate bound estimation in LTI perturbed systems, Automatica, vol.41, issue.10, pp.411835-1838, 2005.
DOI : 10.1016/j.automatica.2005.04.024

E. Kofman, H. Haimovich, and M. M. Seron, A systematic method to obtain ultimate bounds for perturbed systems, International Journal of Control, vol.18, issue.2, pp.167-178, 2007.
DOI : 10.1109/9.763226

E. Kofman, M. M. Seron, and H. Haimovich, Robust Control Design with Guaranteed State Ultimate Bound, Proceedings of the 3rd International Conference on Integrated Modeling and Analysis in Applied Control and Automation, pp.8-10, 2007.
DOI : 10.1016/j.automatica.2007.10.022
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.4448

E. Kofman, F. Fontenla, H. Haimovich, M. M. Seron, and A. Rosario, Control design with guaranteed ultimate bound for feedback linearizable systems, Aceptado en IFAC World Congress, 2008.
DOI : 10.3182/20080706-5-KR-1001.00041

E. Kofman, M. M. Seron, and H. Haimovich, Control design with guaranteed ultimate bound for perturbed systems, Automatica, vol.44, issue.7, pp.1815-1821, 2008.
DOI : 10.1016/j.automatica.2007.10.022

I. Kolmanovsky and E. G. Gilbert, Theory and computation of disturbance invariant sets for discrete-time linear systems, Mathematical Problems in Engineering, vol.4, issue.4, pp.317-367, 1998.
DOI : 10.1155/S1024123X98000866

. Mayne, On the minimal robust positively invariant set for linear difference inclusions, Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, pp.2296-2301, 2005.

A. Kurzhanski and P. Varaiya, Reachability under uncertainty, Decision and Control Proceedings of the 41st IEEE Conference on, pp.1982-1987, 2002.
DOI : 10.1109/cdc.2002.1184818
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.2454

M. Kvasnica, P. Grieder, M. Baoti´cbaoti´c, and M. Morari, Multi-parametric toolbox (mpt) Hybrid Systems: Computation and Control, pp.121-124, 2004.
DOI : 10.1007/978-3-540-24743-2_30

D. Lapierre and J. Moro, Five past midnight in Bhopal, 2002.

Y. Lee, M. Cannon, and B. Kouvaritakis, Extended invariance and its use in model predictive control, Automatica, vol.41, issue.12, pp.412163-2169, 2005.
DOI : 10.1016/j.automatica.2005.07.012

D. Liberzon, Switching in systems and control, 2003.
DOI : 10.1007/978-1-4612-0017-8

H. Lin and P. J. Antsaklis, Robust controlled invariant sets for a class of uncertain hybrid systems, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., pp.3180-3181, 2002.
DOI : 10.1109/CDC.2002.1184359

J. Linhart, Approximation of a ball by zonotopes using uniform distribution on the sphere, Archiv der Mathematik, vol.41, issue.1, pp.82-86, 1989.
DOI : 10.1007/BF01194876

G. Liu and S. Daley, Optimal-tuning nonlinear PID control of hydraulic systems, Control Engineering Practice, vol.8, issue.9, pp.1045-1053, 2000.
DOI : 10.1016/S0967-0661(00)00042-3

V. Loechner, Polylib: A library for manipulating parameterized polyhedra, 1999.

W. Lombardi, A. Luca, S. Olaru, S. Niculescu, and J. Cheong, Feedback Stabilization and motion synchronization of systems with time-delay in the communication network, Proceedings of the IFAC TDS, 2010.
DOI : 10.3182/20100607-3-CZ-4010.00051
URL : https://hal.archives-ouvertes.fr/hal-00528813

W. Lombardi, S. Olaru, M. Lazar, and S. Niculescu, On positive invariance for delay difference equations, Proceedings of the 2011 American Control Conference, 2011.
DOI : 10.1109/ACC.2011.5991538
URL : https://hal.archives-ouvertes.fr/hal-00592322

W. Lombardi, A. Luca, S. Olaru, and S. I. Niculescu, State admissible sets for discrete systems under delay constraints, Proceedings of the 2010 American Control Conference, pp.5185-5190, 2010.
DOI : 10.1109/ACC.2010.5530697
URL : https://hal.archives-ouvertes.fr/hal-00528800

W. Lombardi, S. Olaru, M. Lazar, and S. I. Niculescu, On positive invariance for delay difference equations, Proceedings of the 2011 American Control Conference, 2010.
DOI : 10.1109/ACC.2011.5991538
URL : https://hal.archives-ouvertes.fr/hal-00592322

D. Looze, J. Weiss, N. Eterno, and . Barrett, An automatic redesign approach for restructurable control systems, IEEE Control Systems Magazine, vol.5, issue.2, pp.16-22, 1985.
DOI : 10.1109/MCS.1985.1104940

K. Loskot, A. Polanski, and R. Rudnicki, Further comments on "Vector norms as Lyapunov functions for linear systems", IEEE Transactions on Automatic Control, vol.43, issue.2, pp.289-291, 1998.
DOI : 10.1109/9.661083

J. Lygeros, On reachability and minimum cost optimal control, Automatica, vol.40, issue.6, pp.917-927, 2004.
DOI : 10.1016/j.automatica.2004.01.012

J. Lygeros, D. N. Godbole, and M. Broucke, A fault tolerant control architecture for automated highway systems, IEEE Transactions on Control Systems Technology, vol.8, issue.2, pp.205-219, 2000.
DOI : 10.1109/87.826792

J. Maciejowski, Modelling and predictive control: Enabling technologies for reconfiguration, Annual Reviews in Control, vol.23, pp.13-23, 1999.
DOI : 10.1016/S1367-5788(99)90051-2

J. M. Maciejowski, Predictive control, 2002.
DOI : 10.1007/BFb0113856

J. M. Maciejowski and C. N. Jones, MPC fault-tolerant flight control case study: Flight 1862, Proceedings of the 4th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, 2003.

J. J. Martinez and C. Canudas-de-wit, Model reference control approach for safe longitudinal control, Proceedings of the 23th American Control Conference, pp.2757-2762, 2004.

J. J. Martinez, M. M. Seron, and J. A. De-doná, Fault-Tolerant Switching Scheme with Multiple Sensor-Controller Pairs, Proc. of the 17th IFAC World Congress, pp.1212-1217, 2008.
DOI : 10.3182/20080706-5-KR-1001.00209
URL : https://hal.archives-ouvertes.fr/hal-00327341

B. Marx, D. Maquin, and J. Ragot, State estimation and fault detection of uncertain systems based on an interval approach, 2010 Conference on Control and Fault-Tolerant Systems (SysTol), pp.720-725, 2010.
DOI : 10.1109/SYSTOL.2010.5676036

Q. David, W. R. Mayne, and . Schroeder, Robust time-optimal control of constrained linear systems, Automatica, vol.33, pp.2103-2118, 1997.

D. Q. Mayne, M. M. Seron, and S. V. Rakovi´crakovi´c, Robust model predictive control of constrained linear systems with bounded disturbances, Automatica, vol.41, issue.2, pp.219-224, 2005.
DOI : 10.1016/j.automatica.2004.08.019

D. Mayne, R. Sv-rakovic, F. Findeisen, and . Allgöwer, Robust output feedback model predictive control of constrained linear systems, Automatica, vol.42, issue.7, pp.1217-1222, 2006.
DOI : 10.1016/j.automatica.2006.03.005

M. Enache, Assistance préventivè a la sortie de voie, 2008.

N. Minoiu-enache, M. Netto, S. Mammar, and B. Lusetti, Driver steering assistance for lane departure avoidance, Control Engineering Practice, vol.17, issue.6, pp.642-651, 2009.
DOI : 10.1016/j.conengprac.2008.10.012
URL : https://hal.archives-ouvertes.fr/hal-00506570

S. Nicoleta-minoiu-enache, S. Mammar, B. Glaser, and . Lusetti, Driver assistance system for lane departure avoidance by steering and differential braking, 6th IFAC Symposium Advances in Automotive Control, pp.12-14, 2010.

I. M. Mitchell, C. J. Bayen, and . Tomlin, A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games, IEEE Transactions on Automatic Control, vol.50, issue.7, pp.947-957, 2005.
DOI : 10.1109/TAC.2005.851439

D. D. Moerder, N. Halyo, J. R. Broussard, and A. K. Caglayan, Application of precomputed control laws in a reconfigurable aircraftflight control system, Journal of Guidance, Control, and Dynamics, vol.12, issue.3, pp.325-333, 1989.
DOI : 10.2514/3.20412

A. Molchanov and E. S. Pyatnitskii, Criteria of asymptotic stability of differential and difference inclusions encountered in control theory, Systems & Control Letters, vol.13, issue.1, pp.59-64, 1989.
DOI : 10.1016/0167-6911(89)90021-2

R. J. Montoya, Restructurable controls. National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1983.

H. Ts-motzkin, . Raiffa, and . Thompson, The double description method. Contributions to the theory of games, p.51, 1959.

M. Nagai, H. Mouri, and P. Raksincharoensak, Vehicle lane-tracking control with steering torque input In The Dynamics of Vehicles on Roads and on Tracks, Proceedings of the 17th Iavsd Symposium Held in Lyngby, Denmark, pp.267-278, 2001.

K. Nagpal, J. Abedor, and K. Poolla, An LMI approach to peak-to-peak gain minimisation: filtering and control, Proceedings of 1994 American Control Conference, ACC '94, pp.742-746, 1994.
DOI : 10.1109/ACC.1994.751839

K. S. Narendra and A. M. Annaswamy, Stable adaptive systems, 1989.

F. , N. Akhi-elarab, V. Puig-cayuela, S. Montes-de-oca, and A. Sadeghzadeh, Passive robust fault detection for interval lpv systems using zonotopes, 2009.

Y. Nesterov and A. Nemirovsky, Interior point polynomial methods in convex programming, Studies in applied mathematics, vol.13, 1994.

N. Hoai, S. Nguyen, and . Olaru, Hybrid modelling and constrained control of juggling systems, International Journal of Systems Science, vol.0, issue.0, pp.1-15, 2011.

H. Niemann and J. Stoustrup, Passive fault tolerant control of a double inverted pendulum???a case study, Control Engineering Practice, vol.13, issue.8, pp.1047-1059, 2005.
DOI : 10.1016/j.conengprac.2004.11.002

J. Nocera, Bp ignored the omens of disaster. The New York Times, 2010.

C. Ocampo-martinez, J. A. De-doná, and M. Seron, Actuator fault-tolerant control based on set separation, International Journal of Adaptive Control and Signal Processing, vol.10, issue.1, pp.1070-1090, 2010.
DOI : 10.1002/acs.1181

C. Ocampo-martínez, J. A. De-doná, and M. M. Seron, Actuator Fault-Tolerant Control based on Invariant Set Separation, Proc. of the 17th IFAC World Congress, pp.7276-7281, 2008.
DOI : 10.3182/20080706-5-KR-1001.01231

P. F. Odgaard, J. Stoustrup, and M. Kinnaert, Fault Tolerant Control of Wind Turbines? a benchmark model, Proc. of the 7th IFAC Symp. on Fault Detection, Supervision and Safety of Technical Processes, pp.155-160, 2009.

P. F. Odgaard, P. B. Thøgersen, and J. Stoustrup, Fault isolation in parallel coupled wind turbine converters, 2010 IEEE International Conference on Control Applications, pp.1069-1072, 2010.
DOI : 10.1109/CCA.2010.5611264

S. Olaru and D. Dumur, Avoiding constraints redundancy in predictive control optimization routines, IEEE Transactions on Automatic Control, vol.50, issue.9, pp.1459-1465, 2005.
DOI : 10.1109/TAC.2005.854659

S. Olaru, J. A. De-doná, and M. M. Seron, Positive invariant sets for fault tolerant multisensor control schemes, Proc. of the 17th IFAC World Congress, pp.1224-1229, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00293927

S. Olaru, F. Stoican, J. A. De-doná, and M. M. Seron, Necessary and Sufficient Conditions for Sensor Recovery in a Multisensor Control Scheme, Proc. of the 7th IFAC Symp. on Fault Detection, Supervision and Safety of Technical Processes, pp.977-982, 2009.
DOI : 10.3182/20090630-4-ES-2003.00161
URL : https://hal.archives-ouvertes.fr/hal-00418339

S. Olaru, J. A. De-doná, M. M. Seron, and F. Stoican, Positive invariant sets for fault tolerant multisensor control schemes, International Journal of Control, vol.40, issue.12, pp.2622-2640, 2010.
DOI : 10.1016/j.automatica.2004.01.014
URL : https://hal.archives-ouvertes.fr/hal-00293927

A. J. Osiadacz, G. L. Nemhauser, and L. A. Wolsey, Integer and combinatorial optimization, George L. Nemhauser and Laurence A. Wolsey, Wiley-Interscience Series in Discrete Mathematics and Optimization, New York, 1988, ISBN 0-471-82819-X, 763pp, ??71.90, International Journal of Adaptive Control and Signal Processing, vol.4, issue.4, pp.333-334, 1988.
DOI : 10.1002/acs.4480040410

J. Ousingsawat and M. E. Campbell, Establishing Trajectories for Multi-Vehicle Reconnaissance, AIAA Guidance, Navigation, and Control Conference and Exhibit, pp.2188-2199, 2004.
DOI : 10.2514/6.2004-5224

R. J. Patton, Robustness in Model-Based Fault Diagnosis, pp.103-123, 1997.
DOI : 10.1016/B978-0-08-036201-4.50139-9

H. Peng, W. Zhang, M. Tomizuka, and S. Shladover, A Reusability Study of Vehicle Lateral Control System, Vehicle System Dynamics, vol.15, issue.1, pp.259-278, 1994.
DOI : 10.1115/1.3426335

T. E. Pilutti, D. D. Hrovat, and A. G. Ulsoy, Vehicle steering system and method for controlling vehicle direction through differential braking of left and right road wheels, US Patent, vol.6, p.21367, 2000.

U. Pilutti, G. Ulsoy, and D. Hrovat, Vehicle Steering Intervention Through Differential Braking, Journal of Dynamic Systems, Measurement, and Control, vol.120, issue.3, pp.314-321, 1998.
DOI : 10.1115/1.2805402

P. Planchon and J. Lunze, Diagnosis of linear systems with structured uncertainties based on guaranteed state observation, International Journal of Control Automation and Systems, vol.6, issue.3, pp.306-319, 2008.

I. Prodan, F. Stoican, and S. Olaru, Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques, Journal of Optimization Theory and Applications, vol.8, issue.5, 2011.
DOI : 10.1007/s10957-012-0022-9
URL : https://hal.archives-ouvertes.fr/hal-00750934

V. and P. Cayuela, Robust fdi/ftc using set-membership methods and application to real case studies, 2009.

V. Sasa, E. C. Rakovi´crakovi´c, K. I. Kerrigan, D. Q. Kouramas, and . Mayne, Invariant approximations of the minimal robust positively invariant set, IEEE Transactions on Automatic Control, vol.50, issue.3, pp.406-410, 2005.

S. V. Rakovic and M. Fiacchini, Approximate Reachability Analysis for Linear Discrete Time Systems Using Homothety and Invariance, Proc. 17th IFAC World Congress, 2008.
DOI : 10.3182/20080706-5-KR-1001.02592

S. Rakovic and D. Mayne, Set Robust Control Invariance for Linear Discrete Time Systems, Proceedings of the 44th IEEE Conference on Decision and Control, pp.975-980, 2005.
DOI : 10.1109/CDC.2005.1582284

S. Rakovic, K. Kouramas, J. Ec-kerrigan, D. Allwright, and . Mayne, The minimal robust positively invariant set for linear difference inclusions and its robust positively invariant approximations, Automatica, 2005.

C. G. Ramsay, A. J. Bolsover, R. H. Jones, and W. G. Medland, Quantitative risk assessment applied to offshore process installations. Challenges after the piper alpha disaster, Journal of loss prevention in the process industries, pp.317-330, 1994.
DOI : 10.1016/0950-4230(94)80045-6

A. Richards and J. P. How, Aircraft trajectory planning with collision avoidance using mixed integer linear programming, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), pp.1936-1941, 2002.
DOI : 10.1109/ACC.2002.1023918

A. Richards and J. P. How, Model predictive control of vehicle maneuvers with guaranteed completion time and robust feasibility, Proceedings of the 2003 American Control Conference, 2003., pp.4034-4040, 2005.
DOI : 10.1109/ACC.2003.1240467

J. H. Richter, Reconfigurable Control of Nonlinear Dynamical Systems: A Fault-hiding Approach, 2011.
DOI : 10.1007/978-3-642-17628-9

J. Richter, W. Heemels, N. Van-de-wouw, and J. Lunze, Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking, Automatica, vol.47, issue.4, 2011.
DOI : 10.1016/j.automatica.2011.01.048

A. Rubinov, Radiant Sets and Their Gauges, 2000.
DOI : 10.1007/978-1-4757-3137-8_10
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.9674

A. M. Rubinov and E. V. Sharikov, Star-shaped separability with applications, Journal of Convex Analysis, vol.13, issue.34, p.849, 2006.

A. Rubinov and A. Shveidel, Separability of Star-Shaped Sets with Respect to Infinity, Progress in optimization: contributions from Australasia, p.45, 2000.
DOI : 10.1007/978-1-4613-0301-5_3

A. Rubinov and A. Yagubov, The space of star-shaped sets and its applications in nonsmooth optimization, Mathematical Programming Study, vol.29, pp.175-202, 1986.
DOI : 10.1007/BFb0121146

P. Saint-pierre, Approximation of the viability kernel, Applied Mathematics & Optimization, vol.14, issue.3, pp.187-209, 1994.
DOI : 10.1007/BF01204182

A. V. Savkin and R. J. Evans, Hybrid Dynamical Systems: Controller and Sensor Switching Problems, 2002.
DOI : 10.1007/978-1-4612-0107-6

R. Schneider, Convex bodies: the Brunn-Minkowski theory, 1993.
DOI : 10.1017/CBO9780511526282

T. Schouwenaars, B. De-moor, E. Feron, and J. How, Mixed integer programming for multi-vehicle path planning, Proceedings of the 2nd IEEE European Control Conference, pp.2603-2608, 2001.

F. Scibilia, S. Olaru, and M. Hovd, On feasible sets for MPC and their approximations, Automatica, vol.47, issue.1, 2010.
DOI : 10.1016/j.automatica.2010.10.022
URL : https://hal.archives-ouvertes.fr/hal-00657848

M. María, X. W. Seron, J. A. Zhuo, J. J. Doná, and . Martinez, Multisensor switching control strategy with fault tolerance guarantees, Automatica, vol.44, issue.1, pp.88-97, 2008.

M. María, J. A. Seron, S. De-doná, and . Olaru, Multisensor fault tolerant control allowing sensor healthy-to-faulty and faulty-to-healthy transitions, 2009.

M. Shimakage, S. Satoh, K. Uenuma, and H. Mouri, Design of lane-keeping control with steering torque input, JSAE Review, vol.23, issue.3, pp.317-323, 2002.
DOI : 10.1016/S0389-4304(02)00194-7

M. Smaoui, X. Brun, and D. Thomasset, A study on tracking position control of an electropneumatic system using backstepping design, Control Engineering Practice, vol.14, issue.8, pp.923-933, 2006.
DOI : 10.1016/j.conengprac.2005.05.003
URL : https://hal.archives-ouvertes.fr/hal-00140642

N. Stankovic, S. Olaru, and S. Niculescu, Further remarks on invariance properties of time-delay and switching systems, International Conference on Informatics in Control, Automation and Robotics, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00593065

G. Stein, Respect the unstable Control Systems Magazine, IEEE, vol.23, issue.4, pp.12-25, 2003.

F. Stoican and S. Olaru, Fault tolerant positioning system for a multisensor control scheme, 2010 IEEE International Conference on Control Applications, pp.1051-1056, 2010.
DOI : 10.1109/CCA.2010.5611187
URL : https://hal.archives-ouvertes.fr/hal-00528731

F. Stoican, S. Olaru, M. Nesic, and S. Marinkovic, Control design of a positioning system upon a fault tolerant multisensor scheme, Proceedings of the 17th Telecommunications forum TELFOR, pp.685-688, 2009.

F. Stoican, S. Olaru, and G. Bitsoris, A fault detection scheme based on controlled invariant sets for multisensor systems, 2010 Conference on Control and Fault-Tolerant Systems (SysTol), pp.468-473, 2010.
DOI : 10.1109/SYSTOL.2010.5675958
URL : https://hal.archives-ouvertes.fr/hal-00528740

F. Stoican, S. Olaru, J. A. De-doná, and M. M. Seron, Improvements in the sensor recovery mechanism for a multisensor control scheme, Proceedings of the 2010 American Control Conference, pp.4052-4057
DOI : 10.1109/ACC.2010.5530512
URL : https://hal.archives-ouvertes.fr/hal-00528777

F. Stoican, S. Olaru, M. M. Seron, and J. A. De-doná, A fault tolerant control scheme based on sensor switching and dwell time, Proceedings of the 49th IEEE Conference on Decision and Control, pp.15-17, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00528736

F. Stoican, S. Olaru, M. M. Seron, and J. A. De-doná, Reference governor for tracking with fault detection capabilities, 2010 Conference on Control and Fault-Tolerant Systems (SysTol), pp.546-551, 2010.
DOI : 10.1109/SYSTOL.2010.5675962
URL : https://hal.archives-ouvertes.fr/hal-00528744

F. Stoican, N. Minoiu-enache, and S. Olaru, A lane control mechanism with fault tolerant control capabilities, IEEE Conference on Decision and Control and European Control Conference, 2011.
DOI : 10.1109/CDC.2011.6161317
URL : https://hal.archives-ouvertes.fr/hal-00657862

F. Stoican, I. Prodan, and S. Olaru, On the hyperplanes arrangements in mixed-integer techniques, Proceedings of the 2011 American Control Conference, 2011.
DOI : 10.1109/ACC.2011.5990908
URL : https://hal.archives-ouvertes.fr/hal-00750934

F. Stoican, I. Prodan, and S. Olaru, Enhancements on the hyperplane arrangements in mixed integer techniques, IEEE Conference on Decision and Control and European Control Conference, 2011.
DOI : 10.1109/CDC.2011.6161361
URL : https://hal.archives-ouvertes.fr/hal-00657868

F. Stoican, S. Catalin-florentin-raduinea, and . Olaru, Adaptation of set theoretic methods to the fault detection of a wind turbine benchmark, Proceedings of the 18th IFAC World Congress, pp.8322-8327, 2011.
DOI : 10.3182/20110828-6-IT-1002.01842
URL : https://hal.archives-ouvertes.fr/hal-00592382

F. Stoican, S. Olaru, M. M. Seron, and J. A. De-doná, Reference governor design for tracking problems with fault detection guarantees, Journal of Process Control, vol.22, issue.5, 2011.
DOI : 10.1016/j.jprocont.2012.02.004
URL : https://hal.archives-ouvertes.fr/hal-00751228

F. Stoican, S. Olaru, and G. Bitsoris, A fault detection scheme based on controlled invariant sets for multisensor systems, 2010 Conference on Control and Fault-Tolerant Systems (SysTol), 2011.
DOI : 10.1109/SYSTOL.2010.5675958
URL : https://hal.archives-ouvertes.fr/hal-00528740

F. Stoican, S. Olaru, M. M. Seron, and J. A. De-doná, A discussion on sensor recovery techniques for fault tolerant multisensor schemes, International Journal of Systems Science, vol.3, issue.8, 2011.
DOI : 10.1080/00207721.2010.499651
URL : https://hal.archives-ouvertes.fr/hal-01096262

F. Stoican, S. Olaru, M. M. Seron, and J. A. De-doná, A fault tolerant control scheme based on sensor-actuation channel switching and dwell time, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00528736

S. Suryanarayanan and M. Tomizuka, Appropriate Sensor Placement for Fault-Tolerant Lane-Keeping Control of Automated Vehicles, IEEE/ASME Transactions on Mechatronics, vol.12, issue.4, pp.465-471, 2007.
DOI : 10.1109/TMECH.2007.901943

S. Suryanarayanan, M. Tomizuka, and T. Suzuki, Design of Simultaneously Stabilizing Controllers and Its Application to Fault-Tolerant Lane-Keeping Controller Design for Automated Vehicles, IEEE Transactions on Control Systems Technology, vol.12, issue.3, pp.329-339, 2004.
DOI : 10.1109/TCST.2004.825130

C. M. Talbot, I. Papadimitriou, and M. Tomizuka, Fault Tolerant Autonomous Lateral Control for Heavy Vehicles. Institute of Transportation Studies, Research Reports, 2004.

P. Varaiya, Reach Set Computation Using Optimal Control, NATO ASI SERIES F COM- PUTER AND SYSTEMS SCIENCES, vol.170, pp.323-331, 2000.
DOI : 10.1007/978-3-642-59615-5_15

M. Vassilaki, J. Hennet, and G. Bitsoris, Feedback control of linear discrete-time systems under state and control constraints, International Journal of Control, vol.13, issue.6, pp.1727-1735, 1988.
DOI : 10.1109/TAC.1985.1103785

V. Venkatasubramanian, R. Rengaswamy, and S. N. Kavuri, A review of process fault detection and diagnosis, Computers & Chemical Engineering, vol.27, issue.3, pp.313-326, 2003.
DOI : 10.1016/S0098-1354(02)00161-8

V. Venkatasubramanian, R. Rengaswamy, K. Yin, and S. N. Kavuri, A review of process fault detection and diagnosis, Computers & Chemical Engineering, vol.27, issue.3, pp.293-311, 2003.
DOI : 10.1016/S0098-1354(02)00160-6

S. M. Veres, Limited complexity and parallel implementation of polytope updating, American Control Conference, pp.1061-1062, 1992.

S. Veres, Geometric bounding toolbox (gbt) for matlab. Official website: http://www. sysbrain. com, 2003.

I. I. Vrabie, Nagumo viability theorem. revisited. Nonlinear analysis, pp.2043-2052, 2006.

D. K. Wilde, A LIBRARY FOR DOING POLYHEDRAL OPERATIONS, Parallel Algorithms and Applications, vol.15, issue.3-4, pp.137-166, 2000.
DOI : 10.1007/BF02574699
URL : https://hal.archives-ouvertes.fr/inria-00074515

E. Witrant, A. D. Innocenzo, G. Sandou, F. Santucci, M. D. Di-benedetto et al., Wireless ventilation control for large-scale systems: The mining industrial case, International Journal of Robust and Nonlinear Control, vol.1, issue.1, pp.226-251, 2010.
DOI : 10.1002/rnc.1485
URL : https://hal.archives-ouvertes.fr/hal-00417237

A. Yetendje, M. M. Seron, J. A. Doná, and J. J. Martinez, Sensor fault-tolerant control of a magnetic levitation system, International Journal of Robust and Nonlinear Control, vol.80, issue.2, pp.2108-2121, 2010.
DOI : 10.1002/rnc.1572
URL : https://hal.archives-ouvertes.fr/hal-00576657

T. Zaslavsky, Counting the faces of cut-up spaces, Bulletin of the American Mathematical Society, vol.81, issue.5, 1975.
DOI : 10.1090/S0002-9904-1975-13885-7

Y. Zhang and J. Jiang, Integrated active fault-tolerant control using IMM approach, IEEE Transactions on Aerospace and Electronic Systems, vol.37, issue.4, pp.1221-1235, 2001.
DOI : 10.1109/7.976961

Y. Zhang and J. Jiang, Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control, vol.32, issue.2, pp.229-252, 2008.
DOI : 10.1016/j.arcontrol.2008.03.008

M. Gunter and . Ziegler, Lectures on polytopes, 1995.