Stability analysis of discontinuous dynamical systems determined by semigroups

We present Lyapunov stability and boundedness results for discontinuous dynamical systems (DDS) determined by linear and nonlinear semigroups defined on Banach space. DDS of the type considered herein arise in the modeling of a variety of finite dimensional and infinite dimensional systems, including certain classes of hybrid systems, discrete event systems, switched systems, systems subjected to impulse effects, and the like. We apply our results in the analysis of important specific classes of DDS.