Journal of Applied Mathematics
Volume 2012 (2012), Article ID 524271, 22 pages
http://dx.doi.org/10.1155/2012/524271
Research Article

Filtering-Based Fault Detection for Stochastic Markovian Jump System with Distributed Time-Varying Delays and Mixed Modes

Yucai Ding,1 Hong Zhu,1 Shouming Zhong,2 Yuping Zhang,1 and Jianwei Xia3

1School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
3School of Mathematics Science, Liaocheng University, Liaocheng 252000, China

Received 10 May 2012; Revised 10 November 2012; Accepted 13 November 2012

Academic Editor: Jong Hae Kim

Copyright © 2012 Yucai Ding 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 fault detection for stochastic Markovian jump system is considered. The system under consideration involves discrete and distributed time-varying delays, Itô-type stochastic disturbance, and different system and delay modes. The aim of this paper is to design a fault detection filter such that the fault detection system is stochastically stable and satisfies a prescribed disturbance attenuation level. By using a novel Lyapunov functional, a mix-mode-dependent sufficient condition is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.