Journal of Applied Mathematics
Volume 2012 (2012), Article ID 853170, 15 pages
http://dx.doi.org/10.1155/2012/853170
Research Article

Exponential Stabilizability of Switched Systems with Polytopic Uncertainties

Xia Zhang,1,2 Zun-Quan Xia,1 and Yan Gao3

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2School of Information, Zhejiang University of Finance and Economics Dongfang College, Haining 314408, China
3School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 5 October 2012; Revised 8 December 2012; Accepted 10 December 2012

Academic Editor: Piyapong Niamsup

Copyright © 2012 Xia Zhang 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 exponential stabilizability of switched nonlinear systems with polytopic uncertainties is explored by employing the methods of nonsmooth analysis and the minimum quadratic Lyapunov function. The switchings among subsystems are dependent on the directional derivative along the vertex directions of subsystems. In particular, a sufficient condition for exponential stabilizability of the switched nonlinear systems is established considering the sliding modes and the directional derivatives along sliding modes. Furthermore, the matrix conditions of exponential stabilizability are derived for the case of switched linear system and the numerical example is given to show the validity of the synthesis results.