Robust H∞ Control of a Class of Switching Nonlinear Systems with Time-Varying Delay Via T–S Fuzzy Model

This paper considers H∞ control of a class of switching nonlinear systems with time-varying delays via T–S fuzzy model based on piecewise fuzzy weighting-dependent Lyapunov–Krasovskii functionals (PFLKFs). The systems are switching among several nonlinear systems. The Takagi and Sugeno (T–S) fuzzy model is employed to approximate the sub-nonlinear dynamic systems. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a continuous-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T–S fuzzy systems. Average dwell-time approach and PFLKFs methods are utilized for the stability analysis and controller design, and with free fuzzy weighting matrix scheme. Switching and control laws are obtained such that the H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of LMIs which can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example and the control of an uncertain radio-controlled (R/C) hovercraft with time-varying delay are given to demonstrate the efficiency of the proposed method.