Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 291624, 17 pages
Research Article

Robust Stabilization for Stochastic Systems with Time-Delay and Nonlinear Uncertainties

1School of Electrical Engineering and Automation, Shandong Polytechnic University, Jinan 250353, China
2School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Received 17 September 2011; Accepted 3 November 2011

Academic Editor: Weihai Zhang

Copyright © 2012 Zhiguo Yan 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.


This paper deals with the problem of robust stabilization of stochastic systems with time-delay and nonlinear uncertainties via memory state feedback. Based on Lyapunov krasoviskii functional, some sufficient conditions on local (global) stabilization are given in terms of matrix inequalities. In particular, these stabilizable conditions for a class of nonlinear stochastic time-delay systems are derived in the form of linear matrix inequalities, which have the advantage of easy computation. Moreover, the corresponding results are further extended to the stochastic multiple time-delays systems. Finally, an example is presented to show the superiority of memory state feedback controller to memoryless state feedback controller.