Finite-time stability and stabilization for a class of nonlinear discrete-time descriptor switched systems with time-varying delay

This paper is concerned with the finite-time stability analysis and state feedback stabilization controller design for a class of nonlinear discrete-time descriptor switched systems with time-varying delay. First, by using the implicit function theorem and constructing a switched Lyapunov functional, sufficient conditions are developed which guarantee that the nonlinear discrete-time descriptor switched system with time-varying delay is regular, causal, has a unique solution in a neighborhood of the equilibrium point, and is uniformly finite-time stable. Then a delay-dependent condition on the existence of a finite-time state feedback controller is proposed. Finally, two numerical examples are given to show the effectiveness of the proposed methods.