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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 170794, 10 pages
http://dx.doi.org/10.1155/2014/170794
Research Article

Robust Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

1Department of Mathematics, Yangzhou University, Yangzhou 225002, China
2Department of Basis Course, Lianyungang Technical College, Lianyungang 222006, China
3Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4Department of Computer Science, Brunel University, Uxbridge, Middlesex UB8 3PH, UK

Received 14 July 2014; Accepted 1 August 2014; Published 31 August 2014

Academic Editor: Hongli Dong

Copyright © 2014 Yamin Wang 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

In this paper, we consider the robust control problem for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. The parameter uncertainties enter all the system matrices; the stochastic disturbances are both state and control dependent, and the randomly occurring nonlinearities obey the sector boundedness conditions. The purpose of the problem addressed is to design a state feedback controller such that, for all admissible uncertainties, nonlinearities, and time delays, the closed-loop system is robustly asymptotically stable in the mean square, and a prescribed disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and stochastic analysis tools, a linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the existence of the desired controllers, where the conditions are dependent on the lower and upper bounds of the time-varying delays. The explicit parameterization of the desired controller gains is also given. Finally, a numerical example is exploited to show the usefulness of the results obtained.