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

fYear

2009

fDate

24-26 June 2009

Firstpage

1337

Lastpage

1342

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/MED.2009.5164732

Filename

5164732