STABILITY AND STABILIZABILITY OF DISCRETE EVENT DYNAMIC-SYSTEMS

A finite-state automaton is adopted as a model for Discrete Event Dynamic Systems (DEDS). Stability is defined as visiting a given set E infinitely often. Stabilizability is defined as choosing state feedback such that the closed loop system is stable. These notions are proposed as properties of resiliency or error-recovery. An important ingredient in stability is shown to be a notion of transition-function-invariance. Relations between our notions of stability and invariance, and the notions of safety, fairness, livelock, deadlock, etc., in computer science literature are pointed out. Connections are established between our notions of invariance and the classical notions of A-invariance and (A, B)-invariance of linear systems. Polynomial algorithms for testing stability and stabilizability, and for constructing a stabilizing control law are also presented.