Delay-Dependent Decentralized $H_\infty$ Filtering for Discrete-Time Nonlinear Interconnected Systems With Time-Varying Delay Based on the T–S Fuzzy Model

This paper is concerned with the problem of delay-dependent H_∞ filter design for a class of discrete-time nonlinear interconnected system with time-varying delays via the Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy model consists of N time-delay T-S fuzzy subsystems, and a decentralized H_∞ filter is designed for each subsystem. Based on the delay-dependent piecewise Lyapunov-Krasovskii functional (DDPLKF) and with an improved free-weighting matrix technique, the delay-dependent stability and a prescribed H_∞ performance index are guaranteed for the overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities (LMIs) that are numerically feasible. Two numerical examples are given to demonstrate the effectiveness and advantage of the proposed approach.