Vector L 2-Gain and a Small Gain Theorem for Switched Systems

Authors:	Zhao Jun, City University of Hong Kong, China Hill David J., The Australian National University, Australia
Topic:	1.3 Discrete Event and Hybrid Systems
Session:	Switched Dynamic Systems I
Keywords:	Switched systems, Vector L 2-gain, Stability, Feedback interconnection

Abstract

A concept of vector L 2-gain is presented for switched systems.Each subsystem is allowed to have individual input-outputL 2-gain during any time interval when the subsystem isactivated. Stability is derived from this vector L 2-gain forcertain class of control including output feedback. A small gaintheorem for switched systems with vector L 2-gain is establishedwhich provides a tool for analyzing the behavior of feedbackinterconnected switched systems. The small gain condition is givenin terms of the L 2-gains of the coupled activated subsystems.