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A switched fuzzy filter approach to \(H_\infty\) filtering for Takagi-Sugeno fuzzy Markov jump systems with time delay: the continuous-time case. (English) Zbl 1489.93126

Summary: This paper studies the \(H_\infty\) filtering problem for continuous-time T-S fuzzy Markov jump systems with time-varying delay. A switched fuzzy filter approach is proposed for the first time to improve the previous filter solutions independent of the derivative of fuzzy membership functions (FMFs). Furthermore, a novel delay-product-type FMFs-dependent Lyapunov-Krasovskii functional (LKF) is constructed to make full use of the information on FMFs and time delay simultaneously. A parameter-dependent reciprocally convex inequality (PDRCI) is proposed to more accurately estimate the delay-product-type FMFs-dependent LKF. Based on these ingredients, the existence condition and explicit design method of fuzzy \(H_\infty\) filter are both given. Two examples are employed to illustrate the effectiveness of the proposed methods.

MSC:

93E11 Filtering in stochastic control theory
93C42 Fuzzy control/observation systems
93B36 \(H^\infty\)-control
93C43 Delay control/observation systems
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