Applications to a Class of Discrete-Event Systems

We apply the stability theory of dynamical systems presented in Chapters 3 and 4 in the analysis of an important class of discrete-event systems. We show that these discrete-event systems determine dynamical systems. We establish necessary and sufficient conditions for the uniform stability and the uniform asymptotic stability of invariant sets with respect to the class of discrete-event systems considered. We apply these results in the analysis of two specific examples, a manufacturing system and a load balancing problem in a computer network.