B. D. Anderson and J. B. Moore, Optimal control: linear quadratic methods. Courier Corporation, 2007.

M. Bemporad, A. Morari, V. Dua, and E. N. Pistikopoulos, The explicit linear quadratic regulator for constrained systems, Automatica, vol.38, issue.1, pp.3-20, 2002.
DOI : 10.1016/S0005-1098(01)00174-1

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, Constrained regulation of linear systems, Automatica, vol.31, issue.2, pp.223-227, 1995.
DOI : 10.1016/0005-1098(94)E0053-K

F. Blanchini, Ultimate boundedness control for uncertain discretetime systems via set-induced Lyapunov functions Automatic Control, IEEE Transactions on, vol.39, issue.2, pp.428-433, 1994.
DOI : 10.1109/9.272351

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

D. Chmielewski and V. Manousiouthakis, On constrained infinite-time linear quadratic optimal control, Systems & Control Letters, vol.29, issue.3, pp.121-129, 1996.
DOI : 10.1016/S0167-6911(96)00057-6

F. A. Cuzzola, J. C. Geromel, and M. Morari, An improved approach for constrained robust model predictive control, Automatica, vol.38, issue.7, pp.1183-1189, 2002.
DOI : 10.1016/S0005-1098(02)00012-2

J. Daafouz and J. 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

T. Gal, Postoptimal analyses, parametric programming and related topics, 1995.
DOI : 10.1515/9783110871203

E. G. Gilbert and K. T. 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

A. Grancharova and T. A. Johansen, Explicit nonlinear model predictive control: theory and applications, 2012.
DOI : 10.1007/978-3-642-28780-0

M. Gulan, G. Takács, N. A. Nguyen, S. Olaru, P. Rodriguez-ayerbe et al., Efficient Embedded Model Predictive Vibration Control via Convex Lifting, IEEE Transactions on Control Systems Technology, p.2017
DOI : 10.1109/TCST.2017.2764019

P. Gutman and M. Cwikel, An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states Automatic Control, Control Conference (ECC), 2013 European, pp.251-254, 1987.

Z. P. Jiang and Y. Wang, Input-to-state stability for discrete-time nonlinear systems, Automatica, vol.37, issue.6, pp.857-869, 2001.
DOI : 10.1016/S0005-1098(01)00028-0

E. C. Kerrigan, Robust constraint satisfaction: Invariant sets and predictive control, 2001.

H. K. Khalil, Nonlinear systems, p.323, 2002.

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

M. V. Kothare, V. Balakrishnan, and M. Morari, Robust constrained model predictive control using linear matrix inequalities, Automatica, vol.32, issue.10, pp.1361-1379, 1996.
DOI : 10.1016/0005-1098(96)00063-5

URL : https://authors.library.caltech.edu/28091/1/CDS95-011.pdf

A. M. Lyapunov, Probì eme général de la stabilité du mouvement, Annales de la Faculté des Sciences de Toulouse, pp.203-474, 1907.

D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. Scokaert, Constrained model predictive control: Stability and optimality, Automatica, vol.36, issue.6, pp.789-814, 2000.
DOI : 10.1016/S0005-1098(99)00214-9

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

H. Nguyen, P. Gutman, S. Olaru, and M. Hovd, Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints, Automatica, vol.49, issue.9, pp.2754-2759, 2013.
DOI : 10.1016/j.automatica.2013.05.007

URL : https://hal.archives-ouvertes.fr/hal-00917676

N. A. Nguyen, M. Gulan, S. Olaru, and P. Rodriguez-ayerbe, Convex lifting: Theory and control applications Automatic Control Available: https://halcentralesupelec .archives-ouvertes Any discontinuous PWA function is optimal solution to a parametric linear programming problem, 54th IEEE Conference on Decision and Control, 2015.
DOI : 10.1109/tac.2017.2737234

N. A. Nguyen and S. Olaru, A family of piecewise affine control Lyapunov functions, Automatica, vol.90, pp.212-219, 2018.
DOI : 10.1016/j.automatica.2017.12.052

URL : https://hal.archives-ouvertes.fr/hal-01692257

N. A. Nguyen, S. Olaru, P. Rodriguez-ayerbe, M. Hovd, and I. Necoara, Constructive Solution of Inverse Parametric Linear/Quadratic Programming Problems, Journal of Optimization Theory and Applications, vol.36, issue.9, pp.623-648, 2017.
DOI : 10.1109/9.83532

URL : https://hal.archives-ouvertes.fr/hal-01408472

N. A. Nguyen, S. Olaru, P. Rodríguez-ayerbe, and M. Kvasnica, Convex liftings-based robust control design, Automatica, vol.77, pp.206-213, 2017.
DOI : 10.1016/j.automatica.2016.11.031

URL : https://hal.archives-ouvertes.fr/hal-01509316

R. Oberdieck and E. N. Pistikopoulos, Explicit hybrid model-predictive control: The exact solution, Automatica, vol.58, pp.152-159, 2015.
DOI : 10.1016/j.automatica.2015.05.021

S. V. Rakovic and M. Baric, Parameterized Robust Control Invariant Sets for Linear Systems: Theoretical Advances and Computational Remarks, IEEE Transactions on Automatic Control, vol.55, issue.7, pp.1599-1614, 2010.
DOI : 10.1109/TAC.2010.2042341

S. V. Rakovic, E. C. Kerrigan, K. I. Kouramas, and D. Q. Mayne, Invariant approximations of the minimal robust positively Invariant set, IEEE Transactions on Automatic Control, vol.50, issue.3, pp.406-410, 2005.
DOI : 10.1109/TAC.2005.843854

G. Valmorbida, L. Zaccarian, S. Tarbouriech, I. Queinnec, and A. Papachristodoulou, Nonlinear Static State Feedback for Saturated Linear Plants via a Polynomial Approach, IEEE Transactions on Automatic Control, vol.62, issue.1, pp.469-474, 2017.
DOI : 10.1109/TAC.2016.2566879

URL : https://hal.archives-ouvertes.fr/hal-01576297

M. Vatani, M. Hovd, and S. Olaru, Control design for discrete-time bilinear systems using the scalarized Schur complement, International Journal of Robust and Nonlinear Control, vol.30, issue.5, 2017.
DOI : 10.1109/TPWRD.2015.2412151

URL : https://hal.archives-ouvertes.fr/hal-01719796

V. I. Zubov and L. F. Boron, Methods of AM Lyapunov and their application, 1964.