Finite-time reliable filtering for Takagi–Sugeno fuzzy semi-Markovian jump systems

Abstract

In this study, we concentrate on the problem of a finite-time reliable filter design for discrete-time Takagi–Sugeno fuzzy semi-Markovian jump systems with time-varying delay, sensor faults and randomly occurring uncertainties. To be precise, the time-varying transition probability matrices for the considered system are described by a semi-Markov process. Specifically, the objective is to design a reliable filter ensuring the strict dissipativity performance of the augmented filtering error system in the presence of sensor failures. Further, the stochastic variables describing the random nature of the parameter uncertainties are assumed to follow the Bernoulli distribution. A new finite-time stochastic stability criterion based on reciprocally convex approach and Lyapunov–Krasovskii stability theory is established in terms of linear matrix inequalities for the considered Takagi–Sugeno fuzzy semi-Markovian jump systems. Moreover, the delay-dependent conditions are established to guarantee the augmented filtering error system to be stochastically finite-time bounded and to achieve a prescribed strict dissipativity performance level for all admissible uncertainties and sensor faults. Finally, a numerical example is provided to show the correctness and effectiveness of the proposed method.