Title :
On the existence of a Lyapunov function for a family of switching systems
Author :
Martin, Clyde F. ; Dayawansa, Wijesuriya P.
Author_Institution :
Dept. of Math., Texas Tech. Univ., Lubbock, TX, USA
Abstract :
We consider a system in which the dynamics at any given time is governed by one of a fixed finite family of linear systems, and that switching between these is completely arbitrary. We show that asymptotic stability for all switching paths is equivalent to the existence of a common Lyapunov function for all systems in the family. Via an example it is shown that this Lyapunov function may fail to be quadratic
Keywords :
Lyapunov methods; asymptotic stability; discrete time systems; dynamics; linear systems; Lyapunov function; asymptotic stability; dynamics; feedback; linear systems; switching paths; switching systems; Asymptotic stability; Biological control systems; Biological system modeling; Ear; Environmental factors; Lyapunov method; Mathematics; Mobile robots; Switching systems; Systems engineering and theory;
Conference_Titel :
Decision and Control, 1996., Proceedings of the 35th IEEE Conference on
Conference_Location :
Kobe
Print_ISBN :
0-7803-3590-2
DOI :
10.1109/CDC.1996.572832
