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The topic of this manuscript is the stability analysis of continuous-timeswitched nonlinear systems with constraints on the admissible switchingsignals. Our particular focus lies in considering signals characterized byupper and lower bounds on the length of the switching intervals. We adapt andextend the existing theory of multiple Lyapunov functions, providing converseresults and thus a complete characterization of uniform stability for thisclass of systems. We specify our results in the context of switched linearsystems, providing the equivalence of exponential stability and the existenceof multiple Lyapunov norms. By restricting the class of candidate Lyapunovfunctions to the set of quadratic functions, we are able to providesemidefinite-optimization-based numerical schemes to check the proposedconditions. We provide numerical examples to illustrate our approach andhighlight its advantages over existing methods.

Converse Lyapunov Results for Switched Systems with Lower and Upper Bounds on Switching Intervals