Stability analysis and stabilization of a class of discrete-time nonlinear switched systems with time-delay and affine parametric uncertainty

Abstract

This paper presents stability analysis and stabilization of a nonlinear switched system with subsystems which involve time-varying delay, nonlinear terms, and affine parametric uncertainties. The main goal of this paper is to construct a state-feedback controller to stabilize the closed-loop switched system, and as a special case to derive sufficient conditions to guarantee the stability of the uncontrolled switched system. In this regard, based on switched Lyapunov functions, an appropriate Lyapunov–Krasovskii functional is constructed to establish the sufficient conditions; these conditions depend only on the upper bounds of the time-delay, uncertain parameters, and the maximal bound of the nonlinear term. Finally, numerical examples are provided to verify the theoretical results and to compare the obtained results with previous researches.