Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 289678, 12 pages
doi:10.1155/2010/289678
Research Article

Invariant Sets of Hybrid Autonomous Systems with Disturbance

Li Jian-Qiang,1 Zhu Zexuan,1 Ji Zhen,1 and Pei Hai-Long2

1Shenzhen City Key Laboratory of Embedded System Design, College of Computer Science and Software Engineering, Shenzhen 518060, China
2Department of Automation, South China University of Technology, Guangzhou 510641, China

Received 26 August 2010; Revised 24 October 2010; Accepted 4 November 2010

Academic Editor: G. Rega

Copyright © 2010 Li Jian-Qiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The concept and model of hybrid systems are introduced. Invariant sets introduced by LaSalle are proposed, and the concept is extended to invariant sets in hybrid systems which include disturbance. It is shown that the existence of invariant sets by arbitrary transition in hybrid systems is determined by the existence of common Lyapunov function in the systems. Based on the Lyapunov function, an efficient transition method is proposed to ensure the existence of invariant sets. An algorithm is concluded to compute the transition mode, and the invariant set can also be computed as a convex problem. The efficiency and correctness of the transition algorithm are demonstrated by an example of hybrid systems.