Stability analysis of discrete-time switched systems via Multi-step multiple Lyapunov-like functions

In this paper, we propose a Multi-step multiple Lyapunov-like functions (MLFs) based approach to prove the stability and asymptotic stability of discrete-time switched systems under pre-given time-dependent switching signals. We start with the definition of Multi-step MLFs, which is a relaxation of traditional MLFs. Then, for a discrete-time switched nonlinear system (SNS) under a given time-dependent switching signal, several sufficient conditions for its stability and asymptotic stability are successively provided by using either Multi-step MLFs or strengthened Multi-step MLFs, respectively. Afterwards, for a discrete-time switched linear system with a special time-dependent switching signal, we derive two less conservative linear matrix inequality based criteria for demonstrating its asymptotic stability. In the end, three examples are given to illustrate the applicability and advantage of our relaxed results.