New Results on Decentralized H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{H}}_{\infty }$$\end{document} Fuzzy Filtering Design for Continuous-Time Large-Scale Nonlinear Systems with Time-Varying Delay

This paper studies the problem of decentralized H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{H}}_{\infty }$$\end{document} 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 H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{H}}_{\infty }$$\end{document} 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 H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{H}}_{\infty }$$\end{document} 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 H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\fancyscript{H}}_{\infty }$$\end{document} fuzzy filtering design in terms of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the effectiveness of the proposed method.