A switched fuzzy filter approach to H∞ filtering for Takagi-Sugeno fuzzy Markov jump systems with time delay: The continuous-time case

Abstract

Abstract This paper studies the H ∞ 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 ∞ filter are both given. Two examples are employed to illustrate the effectiveness of the proposed methods.