V. Andrieu and S. Tarbouriech, Global Asymptotic Stabilization for a Class of Bilinear Systems by Hybrid Output Feedback, IEEE Transactions on Automatic Control, vol.58, issue.6, pp.1602-1608, 2013.
DOI : 10.1109/TAC.2012.2229842

URL : https://hal.archives-ouvertes.fr/hal-00647571

P. J. Antsaklis, Hybrid Control Systems: An Introductory Discussion to the Special Issue, IEEE Transactions on Automatic Control, vol.43, issue.4, pp.457-460, 1998.
DOI : 10.1109/TAC.1998.664148

J. P. Aubin and A. Cellina, Differential inclusions: set-valued maps and viability theory, 1984.

A. Bacciotti and L. Rosier, Liapunov functions and stability in control theory, 2006.
DOI : 10.1007/b139028

URL : https://hal.archives-ouvertes.fr/hal-00139067

A. G. Beccuti, S. Mariéthoz, S. Cliquennois, S. Wang, and M. Morari, Explicit Model Predictive Control of DC???DC Switched-Mode Power Supplies With Extended Kalman Filtering, IEEE Transactions on Industrial Electronics, vol.56, issue.6, pp.1864-1874, 2009.
DOI : 10.1109/TIE.2009.2015748

S. C. Bengea and R. A. Decarlo, Optimal control of switching systems, Automatica, vol.41, issue.1, pp.11-27, 2005.

P. Bolzern and W. Spinelli, Quadratic stabilization of a switched affine system about a nonequilibrium point, American Control Conference, pp.3890-3895, 2004.

S. P. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM, vol.15, 1994.
DOI : 10.1137/1.9781611970777

M. S. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control, vol.43, issue.4, pp.475-482, 1998.
DOI : 10.1109/9.664150

J. Cortes, Discontinuous dynamical systems, IEEE Control Systems Magazine, vol.28, issue.3, pp.36-73, 2008.
DOI : 10.1109/MCS.2008.919306

G. S. Deaecto, M. Souza, and J. C. , Chattering free control of continuous-time switched linear systems, IET Control Theory & Applications, vol.8, issue.5, pp.348-354, 2014.
DOI : 10.1049/iet-cta.2013.0065

G. S. Deaecto, J. C. Geromel, and J. Daafouz, Dynamic output feedback H? control of switched linear systems, Automatica, issue.8, pp.47-1713, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00594997

G. S. Deaecto, J. C. Geromel, F. S. Garcia, and J. A. Pomilio, Switched affine systems control design with application to DC???DC converters, IET Control Theory & Applications, vol.4, issue.7, pp.1201-1210, 2010.
DOI : 10.1049/iet-cta.2009.0246

D. L. Elliott, Bilinear control systems: matrices in action, 2009.
DOI : 10.1023/b101451

A. F. Filippov and F. M. Arscott, Differential equations with discontinuous righthand sides: control systems, 1988.
DOI : 10.1007/978-94-015-7793-9

C. Fiter and E. Fridman, Stability of piecewise affine systems with state-dependent delay, and application to congestion control, 52nd IEEE Conference on Decision and Control, pp.1572-1577, 2013.
DOI : 10.1109/CDC.2013.6760106

URL : https://hal.archives-ouvertes.fr/hal-00849844

B. Gerard, H. Souley-ali, M. Zasadzinski, and M. Darouach, ${\cal H}_{\infty }$ Filter for Bilinear Systems Using LPV Approach, IEEE Transactions on Automatic Control, vol.55, issue.7, pp.1668-1674, 2010.
DOI : 10.1109/TAC.2010.2046075

J. C. Geromel and P. Colaneri, Stability and Stabilization of Continuous???Time Switched Linear Systems, SIAM Journal on Control and Optimization, vol.45, issue.5, pp.1915-1930, 2006.
DOI : 10.1137/050646366

R. Goebel, R. G. Sanfelice, and A. R. Teel, Hybrid Dynamical Systems: modeling, stability, and robustness, 2012.

J. M. Gonçalves, A. Megretski, and M. Dahleh, Global stability of relay feedback systems, IEEE Transactions on Automatic Control, vol.46, issue.4, pp.550-562, 2001.
DOI : 10.1109/9.917657

S. Govindaswamy, L. Hetel, A. Polyakov, and T. Floquet, On relay control for discrete time systems using linear matrix inequalities, 2014 European Control Conference (ECC), pp.2225-2230, 2014.
DOI : 10.1109/ECC.2014.6862524

P. Hauroigné, P. Riedinger, and C. Iung, Switched Affine Systems Using Sampled-Data Controllers: Robust and Guaranteed Stabilization, IEEE Transactions on Automatic Control, vol.56, issue.12, pp.2929-2935, 2011.
DOI : 10.1109/TAC.2011.2160598

L. Hetel and E. Bernuau, Local Stabilization of Switched Affine Systems, IEEE Transactions on Automatic Control, vol.60, issue.4, pp.1158-1163, 2015.
DOI : 10.1109/TAC.2014.2350211

URL : https://hal.archives-ouvertes.fr/hal-01058070

L. Hetel and E. Fridman, Robust Sampled ??? Data Control of Switched Affine Systems, IEEE Transactions on Automatic Control, vol.58, issue.11, pp.2922-2928, 2013.
DOI : 10.1109/TAC.2013.2258786

L. Hetel, M. Defoort, and M. Djemai, Binary Control Design for a Class of Bilinear Systems: Application to a Multilevel Power Converter, IEEE Transactions on Control Systems Technology, vol.24, issue.2, pp.1-1, 2015.
DOI : 10.1109/TCST.2015.2460696

URL : https://hal.archives-ouvertes.fr/hal-01697940

T. Hu and F. Blanchini, Non-conservative matrix inequality conditions for stability/stabilizability of linear differential inclusions, Automatica, vol.46, issue.1, pp.190-196, 2010.
DOI : 10.1016/j.automatica.2009.10.022

K. H. Johansson, Relay feedback and multivariable control, 1997.

K. H. Johansson, A. Rantzer, and K. J. Strm, Fast switches in relay feedback systems, Automatica, vol.35, issue.4, 1999.
DOI : 10.1016/S0005-1098(98)00160-5

URL : http://kth.diva-portal.org/smash/get/diva2:495799/FULLTEXT01

M. Jungers, C. C. Gonzaga, and J. Daafouz, Min-switching local stabilization for discrete-time switching systems with nonlinear modes. Nonlinear Analysis: Hybrid Systems, pp.18-26, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00786159

B. Kim and M. Lim, Robust H? control method for bilinear systems, International Journal of Control, Automation, and Systems, vol.1, issue.2, pp.171-177, 2003.

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

H. Lin and P. J. Antsaklis, Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results, IEEE Transactions on Automatic Control, vol.54, issue.2, pp.308-322, 2009.
DOI : 10.1109/TAC.2008.2012009

T. Liu and F. Gao, Industrial process identification and control design: step-test and relay-experiment-based methods, 2011.
DOI : 10.1007/978-0-85729-977-2

D. Patino, P. Riedinger, and C. Iung, Practical optimal state feedback control law for continuous-time switched affine systems with cyclic steady state, International Journal of Control, vol.2, issue.7, pp.1357-1376, 2009.
DOI : 10.1007/978-3-642-84379-2

URL : https://hal.archives-ouvertes.fr/hal-00384680

S. Pettersson, Synthesis of switched linear systems, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), pp.5283-5288, 2003.
DOI : 10.1109/CDC.2003.1272477

S. Pettersson and B. Lennartson, Stabilization of hybrid systems using a min-projection strategy, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), pp.223-228
DOI : 10.1109/ACC.2001.945546

A. E. Polyakov, On practical stabilization of systems with delayed relay control. Automation and Remote Control, pp.712331-2344, 2010.

A. Poznyak, A. Polyakov, and V. Azhmyakov, Attractive Ellipsoids in Robust Control, 2014.
DOI : 10.1007/978-3-319-09210-2

URL : https://hal.archives-ouvertes.fr/hal-01088632

A. Rantzer and M. Johansson, Piecewise linear quadratic optimal control, IEEE Transactions on Automatic Control, vol.45, issue.4, pp.629-637, 2000.
DOI : 10.1109/9.847100

URL : http://lup.lub.lu.se/search/ws/files/4552088/625725.pdf

P. Riedinger and I. Morarescu, A numerical framework for optimal control of switched affine systems with state constraint, 4th IFAC Conference on Analysis and Design of Hybrid Systems, pp.141-146, 2012.
DOI : 10.3182/20120606-3-NL-3011.00002

URL : https://hal.archives-ouvertes.fr/hal-00603921

C. Seatzu, D. Corona, A. Giua, and A. Bemporad, Optimal Control of Continuous-Time Switched Affine Systems, IEEE Transactions on Automatic Control, vol.51, issue.5, pp.726-741, 2006.
DOI : 10.1109/TAC.2006.875053

H. Sira-ramírez and R. Silva-ortigoza, Control design techniques in power electronics devices, 2006.

S. Tarbouriech and G. Garcia, Control of uncertain systems with bounded inputs, 1997.
DOI : 10.1007/BFb0032160

S. Tarbouriech, I. Queinnec, T. R. Calliero, and P. L. Peres, Control design for bilinear systems with a guaranteed region of stability: An LMI-based approach, 2009 17th Mediterranean Conference on Control and Automation, pp.809-814, 2009.
DOI : 10.1109/MED.2009.5164643

A. Trofino, D. Assmann, C. C. Scharlau, and D. F. Coutinho, Switching Rule Design for Switched Dynamic Systems With Affine Vector Fields, IEEE Transactions on Automatic Control, vol.54, issue.9, pp.2215-2222, 2009.
DOI : 10.1109/TAC.2009.2026848

A. Trofino, C. C. Scharlau, T. J. Dezuo, D. O. Mauricio, and C. , Stabilizing switching rule design for affine switched systems, IEEE Conference on Decision and Control and European Control Conference, pp.1183-1188, 2011.
DOI : 10.1109/CDC.2011.6160249

A. Trofino, C. C. Scharlau, J. M. Tiago, D. O. Dezuo, and C. Mauricio, Switching rule design for affine switched systems with performance, 51st Conference on Decision and Control, pp.1923-1928, 2012.
DOI : 10.1109/cdc.2012.6427112