  The topic of this manuscript is the stability analysis of continuous-time
switched nonlinear systems with constraints on the admissible switching
signals. Our particular focus lies in considering signals characterized by
upper and lower bounds on the length of the switching intervals. We adapt and
extend the existing theory of multiple Lyapunov functions, providing converse
results and thus a complete characterization of uniform stability for this
class of systems. We specify our results in the context of switched linear
systems, providing the equivalence of exponential stability and the existence
of multiple Lyapunov norms. By restricting the class of candidate Lyapunov
functions to the set of quadratic functions, we are able to provide
semidefinite-optimization-based numerical schemes to check the proposed
conditions. We provide numerical examples to illustrate our approach and
highlight its advantages over existing methods.
