Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 716474, 23 pages
http://dx.doi.org/10.1155/2012/716474
Research Article

H∞ Filtering for a Class of Piecewise Homogeneous Markovian Jump Nonlinear Systems

Yucai Ding,1 Hong Zhu,1 Shouming Zhong,2 Yuping Zhang,1 and Yong Zeng1

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

Received 14 June 2012; Revised 15 August 2012; Accepted 28 August 2012

Academic Editor: Xing-Gang Yan

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

filtering problem for a class of piecewise homogeneous Markovian jump nonlinear systems is investigated. The aim of this paper is to design a mode-dependent filter such that the filtering error system is stochastically stable and satisfies a prescribed disturbance attenuation level. By using a new mode-dependent Lyapunov-Krasovskii functional, mixed mode-dependent sufficient conditions on stochastic stability are formulated in terms of linear matrix inequalities (LMIs). Based on this, the mode-dependent filter is obtained. A numerical example is given to illustrate the effectiveness of the proposed main results.