Common polynomial Lyapunov functions for linear switched systems

SIAM Journal on Control and Optimization

Volumn 45, Issue 1, 2006, Pages 226-245

  Mason, Paolo ^a   Boscain, Ugo ^a   Chitour, Yacine ^b  

^a SISSA   (Italy)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Polynomial Lyapunov functions; Stability; Switched systems; Uncertain systems

Indexed keywords

ASYMPTOTIC STABILITY; LINEAR SYSTEMS; LYAPUNOV METHODS; POLYNOMIALS; SWITCHING SYSTEMS; UNCERTAIN SYSTEMS;

LINEAR SWITCHED SYSTEMS; POLYNOMIAL LYAPUNOV FUNCTIONS;

SWITCHING FUNCTIONS;

EID: 33847035964     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/040613147     Document Type: Article

References (21)

1. A. A. AGRACHEV AND D. LIBERZON, Lie-algebraic stability criteria for switched systems, SIAM J. Control Optim., 40 (2001), pp. 253-269.
2. A. A. AGRACHEV AND YU. L. SACHKOV, Control Theory from the Geometric Viewpoint, Encyclopedia of Math. Sci. 87, Springer-Verlag, Berlin, 2004.
3. D. ANGELI, A note on stability of arbitrarily switched homogeneous systems, Systems Control Lett., to appear.
4. D. ANGELI AND D. LIBERZON, A note on uniform global asymptotic stability of nonlinear switched systems in triangular form, in Proceedings of the 14th International Symposium on Mathematical Theory of Networks and Systems, 2000.
5. A. BACCIOTTI AND F. CERAGIOLI, Closed loop stabilization of planar bilinear switched systems, Internat J. Control, to appear.
6. F. BLANCHINI, Nonquadratic Lyapunov function for robust control, Automatica J. IFAC, 31 (1995), pp. 451-461.
7. F. BLANCHINI AND S. MIANI, A new class of universal Lyapunov functions for the control of uncertain linear systems, IEEE Trans. Automat. Control, 44 (1999), pp. 641-647.
8. U. BOSCAIN, Stability of planar switched systems: The linear single input case, SIAM J. Control Optim., 41 (2002), pp. 89-112.
9. Z. BUBNICKI, Analysis and Decision Making in Uncertain Systems, Comm. Control Engrg. Ser., Springer-Verlag, London, 2004.
10. G. CHESI, A. GARULLI, A. TESI, AND A. VICINO, Homogeneous Lyapunov functions for systems with structured uncertainties, Automatica J. IFAC, 39 (2003), pp. 1027-1035.
11. 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 (1999), pp. 751-760.
12. D. LIBERZON, J. P. HESPANHA, AND A. S. MORSE, Stability of switched systems: A lie-algebraic condition, Systems Control Lett., 37 (1999), pp. 117-122.
13. D. LIBERZON AND A. S. MORSE, Basic problems in stability and design of switched systems, IEEE Control Systems Magazine, 19 (1999), pp. 59-70.
14. D. LIBERZON, Switching in Systems and Control, Systems Control Found. Appl., Birkhäuser, Boston, 2003.
15. A. P. MOLCHANOV AND E. S. PYATNITSKII, Lyapunov functions that specify necessary and sufficient conditions of absolute stability of nonlinear nonstationary control systems. Part I, Autom. Remote Control, 47 (1986), pp. 344-354.
16. A. P. MOLCHANOV AND E. S. PYATNITSKII, Lyapunov functions that specify necessary and sufficient conditions of absolute stability of nonlinear nonstationary control systems. Part II, Autom. Remote Control, 47 (1986), pp. 443-451.
17. A. P. MOLCHANOV AND E. S. PYATNITSKII, Criteria of asymptotic stability of differential and difference inclusions encountered in control theory, Systems Control Lett., 13 (1989), pp. 59-64.
18. A. OLAS, On robustness of systems with structured uncertainties, in Proceedings of the 4th Workshop on Control Mechanics University of Southern California, 1991.
19. R. SHORTEN AND K. NARENDRA, Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order linear time-invariant systems, in Proceedings of the American Control Conference, 1999, pp. 1410-1414.
20. X. XU AND P. J. ANTSAKLIS, Stabilization of second order LTI switched systems, Internat. J. Control, 73 (2000), pp. 1261-1279.
21. A. L. ZELENTSOVSKY, Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems, IEEE Trans. Automat. Control, 39 (1994), pp. 135-138.