Stability analysis of discrete-time switched systems via Multi-step multiple Lyapunov-like functions. (February 2018) - Lu, Junjie; She, Zhikun; Ge, Shuzhi Sam; Jiang, Xin
Abstract: In this paper, we propose a Multi-step multiple Lyapunov-like functions ( MLF s) 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 MLF s, which is a relaxation of traditional MLF s. 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 MLF s or strengthened Multi-step MLF s, 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.