Z. Artstein, Stabilization with relaxed controls, Nonlinear Analysis: Theory, Methods & Applications, vol.7, pp.1163-1173, 1983.

F. Blanchini and S. Miani, A new class of universal Lyapunov functions for the control of uncertain linear systems, IEEE Transactions on Automatic Control, vol.44, issue.3, pp.641-647, 1999.

V. D. Blondel and J. N. Tsitsiklis, When is a pair of matrices mortal?, Information Processing Letters, vol.63, pp.283-286, 1997.
URL : https://hal.archives-ouvertes.fr/inria-00073998

J. Bochi and I. D. Morris, Continuity properties of the lower spectral radius, Proceedings of the London Mathematical Society, vol.110, issue.2, pp.477-509, 2015.

P. Bolzern, P. Colaneri, and G. De-nicolao, H-infinity co-design for discrete-time dual switching linear systems, Proceedings of the European Control Conference (ECC), 2015.

R. W. Brockett, Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, 1983.

J. Buisson, H. Richard, and . Cormerais, On the stabilisation of switching electrical power converters, Proceedings of Hybrid Systems: Computation and Control, pp.184-197, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00772735

F. H. Clarke, Y. S. Ledyaev, E. D. Sontag, and A. I. Subbotin, Asymptotic controllability implies feedback stabilization, IEEE Transactions on Automatic Control, vol.42, issue.10, pp.1394-1407, 1997.

S. Cong, Characterising the stabilisability for second-order linear switched systems, International Journal of Control, vol.86, issue.3, pp.519-528, 2013.

M. Fiacchini, A. Girard, and M. Jungers, On the stabilizability of discrete-time switched linear systems: Novel conditions and comparisons, IEEE Transactions on Automatic Control, vol.61, issue.5, pp.1181-1193, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01185649

M. Fiacchini and M. Jungers, Necessary and sufficient condition for stabilizability of discretetime linear switched systems. A set theory approach, Automatica, vol.50, issue.1, pp.75-83, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00921268

E. Fornasini and M. Valcher, Linear copositive Lyapunov functions for continuous-time positive switched systems, IEEE transactions on automatic control, vol.55, issue.8, pp.1933-1937, 2010.

F. Forni, R. M. Jungers, and R. Sepulchre, Path-complete positivity of switching systems, 2016.

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.

A. Girard, G. Pola, and P. Tabuada, Approximately bisimilar symbolic models for incrementally stable switched systems. Automatic Control, IEEE Transactions on, vol.55, issue.1, pp.116-126, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00306990

N. Guglielmi and V. Protasov, Exact computation of joint spectral characteristics of linear operators, Foundations of Computational Mathematics, pp.1-61, 2012.

E. Hernandez-varga, R. Middleton, P. Colaneri, and F. Blanchini, Discrete-time control for switched positive systems with application to mitigating viral escape, International Journal of Robust and Nonlinear Control, vol.21, issue.10, pp.1093-1111, 2011.

A. Jadbabaie, J. Lin, and S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, vol.48, issue.6, pp.988-1001, 2003.

J. , When is the (co) sine of a rational angle equal to a rational number, 2010.

R. M. Jungers, The joint spectral radius, theory and applications, Lecture Notes in Control and Information Sciences, vol.385, 2009.

R. M. Jungers, On the existence of a bounded trajectory for nonnegative integer systems, Groups, Geometry, and Dynamics, vol.7, issue.2, pp.349-355, 2013.

C. M. Kellett and A. R. Teel, Weak converse Lyapunov theorems and control-Lyapunov functions, SIAM journal on control and optimization, vol.42, issue.6, pp.1934-1959, 2004.

J. Lee, Infinite-horizon joint LQG synthesis of switching and feedback in discrete time, IEEE Transactions on Automatic Control, vol.54, issue.8, pp.1945-1951, 2009.

J. Lee and G. Dullerud, Supervisory control and measurement scheduling for discrete-time linear systems, IEEE Transactions on Automatic Control, vol.56, issue.4, pp.873-879, 2011.

J. Lee and G. E. Dullerud, Uniform stabilization of discrete-time switched and Markovian jump linear systems, Automatica, vol.42, issue.2, pp.205-218, 2006.

D. Liberzon, Switching in Systems and Control, 2003.

D. Liberzon and S. Morse, Basic problems in stability and design of switched systems, IEEE Control Systems, vol.19, issue.5, pp.59-70, 1999.

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.

S. Pettersson, Synthesis of switched linear systems, Proceedings of IEEE Conference on Decision and Control, 2003.

V. Y. Protasov, R. M. Jungers, and V. D. Blondel, Joint spectral characteristics of matrices: a conic programming approach, SIAM Journal on Matrix Analysis and Applications, vol.31, issue.4, pp.2146-2162, 2010.

A. Rantzer, Scalable control of positive systems, European Journal of Control, vol.24, pp.72-80, 2015.

L. Rifford, Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM Journal on Control and Optimization, vol.41, issue.3, pp.659-681, 2002.

A. Seidenberg, A new decision method for elementary algebra, Annals of Mathematics, vol.60, pp.365-374, 1954.

E. Skafidas, R. J. Evans, A. V. Savkin, and I. R. Petersen, Stability results for switched controller systems, Automatica, vol.35, issue.4, pp.553-564, 1999.

E. D. Sontag, A Lyapunov-like characterization of asymptotic controllability, SIAM Journal on Control and Optimization, vol.21, issue.3, pp.462-471, 1983.

D. P. Stanford and J. M. Urbano, Some convergence properties of matrix sets, SIAM Journal on Matrix Analysis and Applications, vol.15, issue.4, pp.1132-1140, 1994.

Z. Sun and S. S. Ge, Switched linear systems: Control and design, 2005.

Z. Sun and S. S. Ge, Stability theory of switched dynamical systems, 2011.

A. Tarski, A decision method for elementary algebra and geometry, 1951.

M. Wicks, P. Peleties, and R. Decarlo, Switched controller synthesis for the quadratic stabilisation of a pair of unstable linear systems, European Journal of Control, vol.4, issue.2, pp.140-147, 1998.

G. Zhai, Quadratic stabilizability of discrete-time switched systems via state and output feedback, Proceedings of IEEE Conference on Decision and Control, 2001.

G. Zhai, H. Lin, and P. J. Antsaklis, Quadratic stabilizability of switched linear systems with polytopic uncertainties, International Journal of Control, vol.76, issue.7, pp.747-753, 2003.

W. Zhang, A. Abate, J. Hu, and M. P. Vitus, Exponential stabilization of discrete-time switched linear systems, Automatica, vol.45, issue.11, pp.2526-2536, 2009.