Reliable Filter Design of Takagi–Sugeno Fuzzy Switched Systems With Imprecise Modes

This paper is concerned with the problem of asynchronous and reliable filter design with performance constraint for nonlinear Markovian jump systems which are modeled as a kind of Takagi–Sugeno fuzzy switched systems. The nonstationary Markov chain is adopted to represent the asynchronous situation between the designed filter and the considered system. By using the mode-dependent Lyapunov function approach and the relaxation matrix technique, a sufficient condition is proposed to ensure the filtering error system, which is a dual randomly switched system, is stochastically stable and satisfies a given ${{l}_{{2}}}{{-}}{{l}_{{\infty }}}$ performance index simultaneously. Two different approaches are developed to construct the asynchronous and reliable filter. Owing to the Finsler’s lemma, the second approach has fewer decision variables and less conservatism than the first one. Finally, two examples are provided to show the correctness and effectiveness of the proposed methods.