Lyapunov Stability of a Class of Discrete Event Systems

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 non-linear 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 we introduce a logical DES model and define stability in the sense of Lyapunov for logical DES. Then we show that a more conventional analysis of stability which employs appropriate Lyapunov functions can be used for logical DES. This standard approach has the advantage of not requiring high computational complexity (as some of the others) but the difficulty lies in specifying the Lyapunov functions. The approach is illustrated on a manufacturing system that processes batches of N different types of parts according to a priority scheme, one of Dijkstra\´s "self-stabilizing" distributed Systems, and a load balancing problem in computer networks.