Stability Analysis of Discrete Event Systems Modeled by Petri Nets Using Unfoldings

Abstract

The stability of discrete event systems (DESs) is a property related to its robustness; a stable DES is guaranteed to reach a set of desired states in a finite number of steps. Algorithms proposed in the literature are useful for analyzing the stability of DES modeled either by finite automata or a constrained subclass of Petri nets (PNs). In this paper, a novel method to decide the stability of safe PNs is presented. It is based on the analysis of the finite complete prefix of the net unfolding rather than the reachability graph. For concurrent systems, the prefix is usually smaller than the reachability graph and then the analysis using the proposed algorithm is more efficient than analyzing the reachability set of the PN. Note to Practitioners —The stability of a discrete event system (DES) is a property that guarantees that the DES will return to the normal operation behavior after a disturbance deviates the system from such a behavior. This is a key property that a controlled DES must fulfill. The algorithms proposed in this paper allow determining efficiently the stability of concurrent DES by analyzing the Petri net structure.