On stability analysis of linear discrete-time switched systems using quadratic Lyapunov functions

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 5629-5633

  Mason, Paolo ^b   Sigalotti, Mario ^b   Daafouz, Jamal ^a  

^a CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

^b UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DISCRETE TIME CONTROL SYSTEMS; LINEAR SYSTEMS; SWITCHING NETWORKS;

LYAPUNOV QUADRATIC STABILITY; QUADRATIC LYAPUNOV FUNCTION; SWITCHED SYSTEMS;

LYAPUNOV FUNCTIONS;

EID: 62749113391     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4434798     Document Type: Conference Paper

References (17)

1. P. Apkarian and P. Gahinet. A convex characterization of gainscheduled hoo controllers. IEEE Trans. Automat. Contr., 40(5):853-864, 1995.
2. R. Barmish. Stabilization of uncertain systems via linear control. IEEE Trans. Automat. Contr., 28(8):848-850, 1983.
3. F. Blanchini and S. Miani. Stabilization of lpv systems: State feedback, state estimation, and duality. SIAM journal on control and optimization, 40(1):76-97, 2004.
4. V. D. Blondel and Y. Nesterov. Computationally efficient approximations of the joint spectral radius. SIAM Journal of Matrix Analysis, 27(1):256-272, 2005.
5. V. D. Blondel and J. N. Tsitsiklis. The boundedness of all products of a pair of matrices is undecidable. Systems Control Lett., 41(2): 135-140, 2000.
6. U. Boscain. Stability of planar switched systems: the linear single input case. SIAM journal on control and optimization, 41:89-112, 2002.
7. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. SIAM, Studies in Applied Mathematics, 1994.
8. J. Daafouz and J. Bernussou. Parameter dependent lyapunov functions for discrete time systems with time varying. Systems and Control Letters, 43(8):355-359, 2001.
9. J. Daafouz, P. Riedinger, and C. Iung. Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Automat. Control, 47(11):1883-1887, 2002.
10. W. P. Dayawansa and C. F. Martin. A converse lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Trans. Automat. Control, 44:751-760, 1999.
11. M. C. de Oliveira and J. C. Geromel. A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence. Systems Control Lett., 54(11): 1131-1134, 2005.
12. E. Feron, P. Apkarian, and P. Gahinet. Analysis and synthesis of robust control systems via parameter-dependent lyapunov functions. IEEE Trans. Automat. Contr., 41(7):1041-1046, 1996.
13. J. C. Geromel and P. Colaneri. Robust stability of time varying polytopic systems. Systems and Control Letters, 55(1):81-85, 2006.
14. D. Liberzon. Switching in Systems and Control. Birkhauser, Boston, MA, Volume in series Systems and Control: Foundations and Applications., 2003.
15. P. Mason, U. Boscain, and Y. Chitour. Common polynomial lyapunov functions for linear switched systems. SIAM journal on control and optimization, 45:226-245, 2006.
16. ∞ control of linear time-varying systems: A state-space approach. SIAM journal on control and optimization, 29:1394-1413, 1991.
17. J. L. Willems. Stability Theory of Dynamical Systems. NELSON, 1970.