Distributed Filtering of Discrete-Time T-S Fuzzy Time-Delay Systems

Abstract

This chapter is concerned with the distributed fuzzy filter design problem for a class of sensor networks described by discrete-time T-S fuzzy systems with time-varying delays and multiple probabilistic packet losses. In the sensor networks, each individual sensor can receive not only the data packets from its own measurement but also from its neighboring sensors’ measurements according to the sensor networked topology. Our attention is focused on the design of distributed fuzzy filters to guarantee the filtering error dynamical system to be mean-square asymptotically stable with an average $\mathcal{H}_{\infty}$ performance. Sufficient conditions for the obtained filtering error dynamics are proposed by applying a comparison model and the scaled small gain theorem. Based on the measurements and estimates of the system states and its neighbors for each sensor, the solution of the parameters of the distributed fuzzy filters is characterized in terms of the feasibility of a convex optimization problem. An illustrative example will be provided to illustrate the effectiveness of the proposed approaches.