Robust stability and H_∞ control problem for 2-D nonlinear uncertain switched system with mixed time-varying delays under fuzzy rules

In this paper, the robust stability and H_∞ control problem of two-dimensional (2-D) nonlinear polytopic uncertain switched system with mixed time-varying delays is studied based on Roesser model, and the nonlinear system is cleverly broken down into linear forms under the Takagi-Sugeno (T-S) fuzzy rules. Assuming its uncertain parameters are given by convex bounded polyhedral domain. First of all, an improved multi-parameter Lyapunov–Krasovskii function (LKF) is proposed to work hard to get additional information related to time delays, so that it is less conservative. Second, using the aforementioned LKF coupled with Finsler’s lemma, finite-sum inequalities, and Jensen inequalities, a new sufficient condition in linear matrix inequalities (LMIs) is derived for robust H_∞ performance analysis of 2-D nonlinear polytopic uncertain switched system. Third, for this system with time delays, a memory-state feedback controller including information about the past of the system state is designed to remove the effect of time delays on the system, and the resulting closed-loop system is robustly asymptotically stable under the specified H_∞ disturbance attenuation level γ . Finally, the superiority and effectiveness of the proposed results are illustrated by simulation examples.