Stability analysis of non-autonomous switched systems based on time-varying scalar functions

In this paper, we investigate asymptotic stability, exponential stability and uniformly exponential stability of non-autonomous switched systems, respectively. Starting with non-autonomous switched linear systems, we firstly provide necessary and sufficient conditions for its asymptotic stability and exponential stability based on the existence of an asymptotically stable function and an exponentially stable function. Successively, a sufficient condition for uniformly exponential stability of a non-autonomous switched linear system is proposed by the existence of an uniformly exponentially stable function. Based on this sufficient condition, we further derive a sufficient condition for local uniformly exponential stability of non-autonomous switched nonlinear systems. In the end, an illustrative example is given to show the applicability of our theoretical results.