Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 392915, 21 pages
doi:10.1155/2010/392915
Research Article

Improved Results on Fuzzy H∞ Filter Design for T-S Fuzzy Systems

Jiyao An,1,2 Guilin Wen,1 and Wei Xu3

1State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Institute of Space Technology, Hunan University, Changsha 410082, China
2School of Computer and Communication, Hunan University, Changsha 410082, China
3Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007 Sydney, Australia

Received 12 July 2010; Accepted 30 July 2010

Academic Editor: Leonid Berezansky

Copyright © 2010 Jiyao An 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 fuzzy H∞ filter design problem for T-S fuzzy systems with interval time-varying delay is investigated. The delay is considered as the time-varying delay being either differentiable uniformly bounded with delay derivative in bounded interval or fast varying (with no restrictions on the delay derivative). A novel Lyapunov-Krasovskii functional is employed and a tighter upper bound of its derivative is obtained. The resulting criterion thus has advantages over the existing ones since we estimate the upper bound of the derivative of Lyapunov-Krasovskii functional without ignoring some useful terms. A fuzzy H∞ filter is designed to ensure that the filter error system is asymptotically stable and has a prescribed H∞ performance level. An improved delay-derivative-dependent condition for the existence of such a filter is derived in the form of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.