Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 431576, 16 pages
http://dx.doi.org/10.1155/2012/431576
Research Article

Robust Reliable 𝐻 ∞ Control for Nonlinear Stochastic Markovian Jump Systems

Guici Chen1 and Yi Shen2

1Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, China
2Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received 29 November 2011; Accepted 2 April 2012

Academic Editor: Weihai Zhang

Copyright © 2012 Guici Chen and Yi Shen. 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 robust reliable 𝐻 ∞ control problem for a class of nonlinear stochastic Markovian jump systems (NSMJSs) is investigated. The system under consideration includes Itô-type stochastic disturbance, Markovian jumps, as well as sector-bounded nonlinearities and norm-bounded stochastic nonlinearities. Our aim is to design a controller such that, for possible actuator failures, the closed-loop stochastic Markovian jump system is exponential mean-square stable with convergence rate 𝛼 and disturbance attenuation 𝛾 . Based on the Lyapunov stability theory and Itô differential rule, together with LMIs techniques, a sufficient condition for stochastic systems is first established in Lemma 3. Then, using the lemma, the sufficient conditions of the solvability of the robust reliable 𝐻 ∞ controller for linear SMJSs and NSMJSs are given. Finally, a numerical example is exploited to show the usefulness of the derived results.