Lyapunov Functions for Shuffle Asymptotic Stability of Discrete-Time Switched Systems

In this letter, we investigate stability of discrete-time switched systems under shuffled switching signals. A switching signal is said to be shuffled if each mode of the switched system is activated infinitely often. We introduce the notion of shuffle Lyapunov functions and show that the existence of such a function is a sufficient condition for global uniform shuffle asymptotic stability. In the second part of this letter, we show that for a specific class of switched systems, with linear and invertible dynamics, existence of a shuffle Lyapunov function is also necessary, even for the weaker notion of global shuffle attractivity. Examples and numerical experiments are used to illustrate the main results of this letter.