Design of static and dynamic output feedback controllers for a discrete-time switched nonlinear system with time-varying delay and parametric uncertainty

Abstract

This study focuses on the stability analysis and design of output feedback controllers for a non-linear discrete-time switched system with uncertain subsystems. The considered system involves time-varying delay, non-linear terms, and affine parametric uncertainties. The main goals of this study are first to derive sufficient conditions to guarantee the stability of the unforced switched system and then, to construct two stabilising output feedback controllers (static and dynamic) to stabilise the closed-loop system with considering arbitrary switching signals. 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 and uncertain parameters. Furthermore, in the proposed method, the admissible bound of time-delay and the maximum non-linearity of subsystems could be calculated. Finally, numerical examples are provided to verify the theoretical results.