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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 523462, 17 pages
http://dx.doi.org/10.1155/2014/523462
Research Article

Robust Nonfragile Filtering for Uncertain T-S Fuzzy Systems with Interval Delay: A New Delay Partitioning Approach

1Key Laboratory of Embedded and Network Computing of Hunan Province, College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
2Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Received 16 April 2014; Revised 27 July 2014; Accepted 6 August 2014; Published 3 September 2014

Academic Editor: Alexander Domoshnitsky

Copyright © 2014 Xianzhong Xia 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

This paper investigates the problem of robust nonfragile fuzzy filtering for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Attention is focused on the design of a filter such that the filtering error system preserves a prescribed performance, where the filter to be designed is assumed to have gain perturbations. By developing a delay decomposition approach, both lower and upper bound information of the delayed plant states can be taken into full consideration; the proposed delay-fractional-dependent stability condition for the filter error systems is obtained based on the direct Lyapunov method allied with an appropriate and variable Lyapunov-Krasovskii functional choice and with tighter upper bound of some integral terms in the derivation process. Then, a new robust nonfragile fuzzy filter scheme is proposed, and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are utilized to demonstrate the effectiveness and reduced conservatism of the proposed approach.