Decentralized piecewise H∞ fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay. Issue 9 (September 2015) - Zhong, Zhixiong; Fu, Shasha; Hayat, Tasawar; Alsaadi, Fuad; Sun, Guanghui
Abstract This paper investigates the problem of decentralized piecewise <alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />H∞</alternatives> 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 <alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />H∞</alternatives> disturbance attenuation level. A two-term approximation method is proposed to transform the filtering error system into an interconnected formulation, and the decentralized <alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />H∞</alternatives> 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 <alternatives><inline-graphic xlink:href="ark:/27927/pgj2ft814wn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />H∞</alternatives> 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.