Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay

Authors:
Ligang Wu;Zidong Wang
Affiliations:
Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, P.R. China;Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex UB8 3PH, UK
Venue:
Signal Processing
Year:
2009

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Abstract

This paper is concerned with the H"~ filtering problem for nonlinear stochastic Takagi-Sugeno (T-S) fuzzy systems with time-varying delay, where the nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent filters that guarantee a prescribed noise attenuation level in an H"~ sense. To reduce the conservatism, a delay-dependent approach developed to derive the main results in terms of linear matrix inequalities (LMIs). When the fuzzy-rule-independent filter is applied, a sufficient condition is first proposed to ensure that the filtering error system is stochastically stable with an H"~ performance. The corresponding solvability condition for a desired fuzzy-rule-independent filter is established by casting the fuzzy-rule-independent filter design into a convex optimization problem. Then, the parallel results are obtained for the case when the fuzzy-rule-dependent filter is used, and these results have less conservatism than those for the fuzzy-rule-independent filter design case. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.