Stability analysis of discontinuous dynamical systems determined by semigroups

Abstract

We present Lyapunov stability 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- 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 several important specific classes of DDS.