New Results on Decentralized $${\fancyscript{H}}_{\infty }$$ H ∞ Fuzzy Filtering Design for Continuous-Time Large-Scale Nonlinear Systems with Time-Varying Delay

Abstract

This paper studies the problem of decentralized $${\fancyscript{H}}_{\infty }$$H? fuzzy filtering design for a class of continuous-time large-scale nonlinear systems with time-varying delay. The considered large-scale system consists of several nonlinear subsystems with interconnections and state delays. Each nonlinear subsystem is represented by a Takagi---Sugeno (T---S) model, and the state delay of each subsystem is assumed to be of an interval-like time-varying form. Attention is focused on designing a decentralized fuzzy filter such that the resulting filtering error system is asymptotically stable with a guaranteed $${\fancyscript{H}}_{\infty }$$H? disturbance attenuation level. We firstly propose a two-term approximation method to transform the filtering error system into an interconnected formulation and reformulate the problem of decentralized $${\fancyscript{H}}_{\infty }$$H? fuzzy filtering design in the context of input---output (IO) stability. Then, based on a Lyapunov---Krasovskii functional (LKF) combined with the scaled small gain (SSG) theorem, less conservative results are presented for the decentralized $${\fancyscript{H}}_{\infty }$$H? fuzzy filtering design in terms of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the effectiveness of the proposed method.