Lyapunov stability of a class of discrete event systems

Abstract

Discrete event systems (DES) are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals. "Logical" DES are a class of discrete time DES with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences. Recently, there has been much interest in studying the stability properties of logical DES and several definitions for stability, and methods for stability analysis have been proposed. Here the authors introduce a logical DES model and define stability in the sense of Lyapunov and asymptotic stability for logical DES. Then the authors show that more conventional analysis of stability which employs appropriate Lyapunov functions can be used for logical DES. The authors provide a general characterization of the stability properties of automata-theoretic DES models, Petri nets, and finite state systems. Furthermore, the Lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of N different types of parts according to a priority scheme (to prove properties related to the machine's ability to reorient itself to achieve safe operation) and a load balancing problem in computer networks (to study the ability of the system to achieve a balanced load to minimize underutilization).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>