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Abstract and Applied Analysis
Volume 2014, Article ID 937495, 12 pages
Research Article

T-S Fuzzy Model-Based Approximation and Filter Design for Stochastic Time-Delay Systems with Hankel Norm Criterion

College of Electrical and Information Engineering, Northeast Petroleum University, Daqing, Heilongjiang Province 163318, China

Received 3 January 2014; Accepted 21 January 2014; Published 4 March 2014

Academic Editor: Shen Yin

Copyright © 2014 Yanhui Li and Xiujie Zhou. 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.


This paper investigates the Hankel norm filter design problem for stochastic time-delay systems, which are represented by Takagi-Sugeno (T-S) fuzzy model. Motivated by the parallel distributed compensation (PDC) technique, a novel filtering error system is established. The objective is to design a suitable filter that guarantees the corresponding filtering error system to be mean-square asymptotically stable and to have a specified Hankel norm performance level . Based on the Lyapunov stability theory and the Itô differential rule, the Hankel norm criterion is first established by adopting the integral inequality method, which can make some useful efforts in reducing conservativeness. The Hankel norm filtering problem is casted into a convex optimization problem with a convex linearization approach, which expresses all the conditions for the existence of admissible Hankel norm filter as standard linear matrix inequalities (LMIs). The effectiveness of the proposed method is demonstrated via a numerical example.