A. Fuller, In-the-large stability of relay and saturating control systems with linear controllers, International Journal of Control, vol.10, pp.457-480, 1969.

E. Sontag and H. Sussmann, Nonlinear output feedback design for linear systems with saturating controls, Proceedings of the 29th IEEE Conference on, vol.6, pp.3414-3416, 1990.

H. Sussmann, E. Sontag, and Y. Yang, A general result on the stabilization of linear systems using bounded controls, IEEE Transactions on, vol.39, issue.12, pp.2411-2425, 1994.

Z. Lin and A. Saberi, Semi-global exponential stabilization of linear systems subject to "input saturation" via linear feedbacks, Systems & Control Letters, vol.21, issue.3, pp.225-239, 1993.

B. Zhou, G. Duan, and Z. Lin, Global stabilization of the double integrator system with saturation and delay in the input, IEEE Transactions on Circuits and Systems-I, vol.57, issue.6, pp.1371-1383, 2010.

D. Henrion, G. Garcia, and S. Tarbouriech, Piecewise-linear robust control of systems with input constraints, European Journal of Control, vol.5, issue.1, pp.157-166, 1999.

G. Valmorbida, L. Zaccarian, S. Tarbouriech, I. Queinnec, and A. Papachristodoulou, A polynomial approach to nonlinear state feedback stabilization of saturated linear systems, Proceedings of the 53rd IEEE Conference on, pp.6317-6322, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01851201

M. Tanaskovic, L. Fagiano, R. Smith, and M. Morari, Adaptive receding horizon control for constrained mimo systems, Automatica, vol.50, pp.3019-3029, 2014.

F. Z. Chaoui, F. Giri, J. M. Dion, M. M-saad, and L. Dugard, Direct adaptive control subject to input amplitude constraint, IEEE Transactions on Automatic Control, vol.45, pp.485-490, 2000.

C. Zhang and E. R. , Continuous direct adaptive control with saturation input constraint, IEEE Transactions on Automatic Control, vol.39, pp.1718-1722, 1994.

P. J. Werbos, Approximate dynamic programming for real time control and neural modelling," in Handbook of Intelligent Control, 1992.

S. Bhasin, R. Kamalapurkar, M. Johnson, K. Vamvoudakis, F. L. Lewis et al., A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems, Automatica, vol.49, pp.82-92, 2013.

M. Abu-khalaf and F. L. Lewis, Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach, Automatica, vol.41, pp.779-791, 2005.

H. Zhang, Y. Luo, and D. Liu, Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints, IEEE Tranactions on Neural Network, vol.20, pp.1490-1503, 2009.

H. Modares, F. L. Lewis, and M. Naghibi-sistani, Adaptive optimal control of unknown constrained-input systems using policy iteration and neural networks, IEEE Transactions on Neural Networks and Learning Systems, vol.24, pp.1513-1525, 2013.

, Online solution of nonquadratic two-player zero-sum games arising in the h ? control of constrained input systems, International Journal of Adaptive Control and Signal Processing, vol.24, pp.232-254, 2013.

J. Lasalle and S. Lefschetz, Stability by Liapunov's direct method: with applications, 1967.

D. Dai, T. Hu, A. R. Teel, and L. Zaccarian, Piecewise-quadratic lyapunov functions for systems with deadzones or saturations, Systems & Control Letters, vol.58, issue.5, pp.365-371, 2009.

D. E. Kirk, Optimal Control Theory: An Introduction, 1970.

R. A. Freeman and P. V. Kokotovic, Inverse optimality in robust stabilization, SIAM Journal on Control and Optimization, vol.34, pp.1365-1391, 1996.

S. Baldi, G. Valmorbida, A. Papachristodoulou, and E. B. Kosmatopoulos, Piecewise polynomial policy iterations for synthesis of optimal control laws in input-saturated systems, Proceedings of the 2015 American Control Conference, 2015.

P. A. Ioannou and J. Sun, Robust Adaptive Control, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01394197

E. B. Kosmatopoulos, An adaptive optimization scheme with satisfactory transient performance, Automatica, vol.45, issue.3, pp.716-723, 2009.

J. Spall, Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control, 2003.

A. Papachristodoulou, J. Anderson, G. Valmorbida, S. Prajna, P. Seiler et al., SOSTOOLS: Sum of squares optimization toolbox for MATLAB, 2013.

P. L. and D. Henrion, Sedumi interface 1.02: a tool for solving lmi problems with sedumi, Proceedings, IEEE International Symposium on Computer Aided Control System Design, pp.272-277, 2002.