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A Geometrical Treatment for Obtaining Necessary and Sufficient Conditions for Joint Quadratic Lyapunov Function Existence for State-Dependent, Switched Systems: A Two-Dimensional Case

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Griggs, Wynita M., King, Christopher K., Shorten, Robert N., Mason, Oliver and Wulff, Kai (2009) A Geometrical Treatment for Obtaining Necessary and Sufficient Conditions for Joint Quadratic Lyapunov Function Existence for State-Dependent, Switched Systems: A Two-Dimensional Case. Control and Automation, 2009. MED '09. 17th Mediterranean Conference on . ISBN 978-1-4244-4684-1. pp. 1337-1342.

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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.

Item Type:	Article
Additional Information:	Copyright © [2009] IEEE.   Reprinted from 17th Mediterranean Conference on Control and Automation, 2009. MED '09.
Keywords:	Lyapunov methods; computational geometry; matrix algebra; set theory; stability; state-space methods; time-varying systems;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	2220
Identification Number:	DOI: 10.1109/MED.2009.5164732
Depositing User:	Oliver Mason
Date Deposited:	27 Oct 2010 16:02
Journal or Publication Title:	Control and Automation, 2009. MED '09. 17th Mediterranean Conference on . ISBN 978-1-4244-4684-1
Publisher:	IEEE
Refereed:	Yes
Related URLs:	http://ieeexplore.ieee.org/Xplore/dynhom...
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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