Decentralized piecewise H∞ fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay

This paper investigates the problem of decentralized piecewise H∞ filtering design for a class of discrete-time large-scale nonlinear systems with time-varying delay. The considered large-scale system consists of a number of nonlinear subsystems, and each nonlinear subsystem is represented by a Takagi-Sugeno (T-S) model. The time-varying state delay of each subsystem is assumed to be of an interval-like type with lower and upper bounds. The objective is to design a decentralized piecewise filter such that the filtering error system is asymptotically stable with a guaranteed H∞ disturbance attenuation level. A two-term approximation method is proposed to transform the filtering error system into an interconnected formulation, and the decentralized H∞ filtering problem is reformulated in the context of input-output (IO) stability. Based on a piecewise Lyapunov-Krasovskii functional (PLKF) combined with the scaled small gain (SSG) theorem, less conservative results are presented for the decentralized piecewise H∞ filtering design of the large-scale T-S fuzzy system in terms of linear matrix inequalities. Two examples are provided to illustrate the effectiveness of the proposed method.