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Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay. (English) Zbl 1178.93141

Summary: This paper is concerned with the \(H_{\infty }\) 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 \(H_{\infty }\) 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 \(H_{\infty }\) 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.

MSC:

93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
93C42 Fuzzy control/observation systems
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