Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 507828, 9 pages
http://dx.doi.org/10.1155/2013/507828
Research Article

Sliding Mode Control for Markovian Switching Singular Systems with Time-Varying Delays and Nonlinear Perturbations

Guowei Yang,1,2 Yonggui Kao,2 and Wei Li2

1College of Information Engineering, Nanchang Hangkong University, Nanchang, Jiangxi 330063, China
2Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China

Received 13 October 2012; Revised 28 December 2012; Accepted 28 December 2012

Academic Editor: Her-Terng Yau

Copyright © 2013 Guowei Yang 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

This paper is devoted to investigating sliding mode control (SMC) for Markovian switching singular systems with time-varying delays and nonlinear perturbations. The sliding mode controller is designed to guarantee that the nonlinear singular system is stochastically admissible and its trajectory can reach the sliding surface in finite time. By using Lyapunov functional method, some criteria on stochastically admissible are established in the form of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness and efficiency of the obtained results.