Decentralized piecewise ℋ<inf>∞</inf> control for large-scale T-S fuzzy systems with time-varying delay

Abstract

The problem of decentralized piecewise ℋ ∞ control for discrete-time large-scale nonlinear systems with time-varying delay is studied. Each nonlinear subsystem in the large-scale system is represented by a Takagi-Sugeno (T-S) model, and the time-varying state delay of each subsystem is assumed to be of an interval-like type. We propose a two-term approximation method to transform the closed-loop fuzzy control system into an interconnected formulation, which is subject to two constant time delays in the forward path and norm-bounded uncertainties in the feedback one. By introducing a piecewise Lyapunov-Krasovskii functional (PLKF) and utilizing the scaled small gain (SSG) theorem, the LMI conditions to the decentralized piecewise memory ℋ ∞ state-feedback controller design for the large-scale fuzzy systems are derived. An example is provided to verify the efficacy of the proposed method.