Stability of discontinuous retarded functional differential equations with applications

We present Lyapunov stability results, including converse theorems, for a class of discontinuous dynamical systems (DDS) determined by the solutions of retarded functional differential equations. We demonstrate the applicability of these results in the analysis of several specific important classes of DDS determined by functional differential equations and differential-difference equations. Index Terms--Asymptotic stability, differential-difference equations, discontinuous dynamical systems (DDS), exponential stability, hybrid systems, Lyapunov stability, retarded functional differential equations, switched systems, systems with delays.