Title :
Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions
Author :
Blanchini, Franco ; Savorgnan, Carlo
Author_Institution :
Dipt. di Matematica e Informatica, Univ. degli Studi di Udine
Abstract :
Counterexamples are given which show that a linear switched system (with controlled switching) that can be stabilized by means of a suitable switching law does not necessarily admit a convex Lyapunov function. Both continuous and discrete-time cases are considered. This fact contributes in focusing the difficulties encountered so far in the theory of stabilization of switched systems. In particular the result is in contrast with the case of uncontrolled switching in which it is known that if a system is stable under arbitrary switching then admits a polyhedral norm as a Lyapunov function
Keywords :
Lyapunov methods; continuous time systems; discrete time systems; linear systems; stability; time-varying systems; Lyapunov function; continuous time; discrete-time; switched linear systems; Control systems; Linear systems; Lyapunov method; Stability; Sufficient conditions; Switched systems; Switches; Switching systems; USA Councils; Uncertain systems;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.376748