Title :
A geometrical treatment for obtaining necessary and sufficient conditions for joint quadratic Lyapunov function existence for state-dependent, switched systems: A two-dimensional case
Author :
Griggs, Wynita M. ; King, Christopher K. ; Shorten, Robert N. ; Mason, Oliver ; Wulff, Kai
Author_Institution :
Hamilton Inst., Nat. Univ. of Ireland, Maynooth, Ireland
Abstract :
The question of existence of joint quadratic Lyapunov functions (QLFs) for state-dependent, switched dynamical systems is given a preliminary geometrical treatment in this paper. The joint QLF problem for a switched system and a collection of regions defined by state vectors that determine when switching occurs consists of finding nonempty intersections of convex sets of QLFs. The existence of a joint QLF guarantees switched system stability. Necessary and sufficient conditions for the existence of a joint QLF are obtained for a two-dimensional problem.
Keywords :
Lyapunov methods; computational geometry; matrix algebra; set theory; stability; state-space methods; time-varying systems; convex set; geometrical treatment; joint quadratic Lyapunov function; matrix algebra; state-dependent switched dynamical system stability; state-space method; Asymptotic stability; Automatic control; Automation; Control systems; Lyapunov method; Sufficient conditions; Switched systems; Switches; Symmetric matrices; Tin;
Conference_Titel :
Control and Automation, 2009. MED '09. 17th Mediterranean Conference on
Conference_Location :
Thessaloniki
Print_ISBN :
978-1-4244-4684-1
Electronic_ISBN :
978-1-4244-4685-8
DOI :
10.1109/MED.2009.5164732
