Equivalence between different stabilities of discrete-time delayed switched systems with uncertainties

This paper mainly addresses the relationship between attractivity, asymptotic stability, and exponential stability of switched systems with delays and uncertainties under four classes of switching signals: Arbitrary switching signals, periodic switching signals, switching signals with constraints of dwell time and average dwell time. The following results are established: If a homogeneous switched system of degree one is robustly uniformly attractive over some class of switching signals, then it is robustly uniformly exponentially stable (and therefore robustly uniformly asymptotically stable) over the same class of switching signals. Applying the result to switched linear systems with delays and uncertainties, one can check their exponential stability by their asymptotic stability.