Sufficient for Arbitrary Switching Stability of Switched Nonlinear Systems

Constrained switching of switched nonlinear systems consists of many classes of switching signals with markedly different features. One of the most important ones is the average dwell time (ADT) switching. For switched systems, it is a well-known result that a switched nonlinear system is globally uniformly asymptotically stable under arbitrary switching sequence if the ADT satisfies the lower bound defined by a real constant value ( ln μ α ). In this note, it will be shown that this ADT condition is also necessary.