Stability of Time-invariant Max-Min-Plus-Scaling Discrete-Event Systems with Diverse States

Abstract

In this paper, we discuss the stability of general time-invariant discrete-event systems modelled as max-min-plus-scaling (MMPS) systems. We analyze MMPS systems with two types of states: time states and quantity states. A set of linear programming problems are proposed to find the growth rates of the time states via a normalization of the MMPS system. Then a framework for stability analysis of the general time-invariant MMPS system is discussed with respect to the normalized system. The approach presented in this paper is an efficient way to study the stability of a general MMPS system.