A notion of dissipativity for discrete event systems

摘要

Dissipativity is a useful tool for analyzing and synthesizing stable feedback systems. Briefly, the property of dissipativity is that a system only stores and dissipates energy, with respect to a given energy storage function, and does not generate its own energy. This property carries a strong reliance on a notion of time that prohibits its direct application to discrete event systems (DES). The current paper takes the concept of dissipativity and applies it to DES by replacing the notion of time with an event-based definition. Two notions of dissipativity are defined, one for finite automata and the other for a general class of DES. For each notion, properties of dissipative DES are shown that connect with existing notions of stability for DES as would be expected from the classical definition of dissipativity. Examples are provided to illustrate the methods covered in the paper.