Decentralized $H_{\infty }$ Filter Design for Discrete-Time Interconnected Fuzzy Systems

This paper describes a decentralized
H

_infin
filter design for discrete-time interconnected fuzzy systems based on piecewise-quadratic Lyapunov functions. The systems consist of
J
discrete-time interconnected Takagi-Sugeno (T-S) fuzzy subsystems, and a decentralized
H

_infin
filter is designed for each subsystem. It is shown that the stability of the overall filtering-error system with
H

_infin
performance can be established if a piecewise-quadratic Lyapunov function can be constructed. Moreover, the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Two simulation examples are given to show the effectiveness of the proposed approach.