A study on stability analysis of discrete event dynamic systems

Abstract

In supervisory control, discrete event dynamic systems (DEDSs) are modeled by finite-state automata, and their behaviors described by the associated formal languages; control is exercised by a supervisor; whose control action is to enable or disable the controllable events. In this paper we present a general stability concept for DEDSs, stability in the sense of Lyapunov with resiliency, by incorporating Lyapunov stability concepts [1], [10] with the concept of stability in the sense of error recovery [8]. We also provide algorithms for verifying stability and obtaining a domain of attraction. Relations between the notion of stability and the notion of fault-tolerance are addressed.