Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 431751, 20 pages
http://dx.doi.org/10.1155/2011/431751
Research Article

Stochastic Finite-Time Guaranteed Cost Control of Markovian Jumping Singular Systems

Yingqi Zhang,1 Caixia Liu,1 and Xiaowu Mu2

1College of Science, Henan University of Technology, Zhengzhou 450001, China
2Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China

Received 17 April 2011; Revised 2 August 2011; Accepted 8 August 2011

Academic Editor: Alexei Mailybaev

Copyright © 2011 Yingqi 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 problem of stochastic finite-time guaranteed cost control is investigated for Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the definitions of stochastic singular finite-time stability, stochastic singular finite-time boundedness, and stochastic singular finite-time guaranteed cost control are presented. Then, sufficient conditions on stochastic singular finite-time guaranteed cost control are obtained for the family of stochastic singular systems. Designed algorithms for the state feedback controller are provided to guarantee that the underlying stochastic singular system is stochastic singular finite-time guaranteed cost control in terms of restricted linear matrix equalities with a fixed parameter. Finally, numerical examples are given to show the validity of the proposed scheme.