Lagrange stability and boundedness of discrete event systems
The authors analyze a class of logical Discrete Event Systems (DES), i.e. a class of discrete-time asynchronous DES, defined on a metric space, with equation of motion that are often non-linear and discontinuous with respect to the random occurrence of events. They extend the conventional Lyapunov framework so that it applies to the study of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability of the above class of logical DES. Within this stability-theoretic framework, they show that the standard Petri net-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, they introduce the notion of uniform ultimate boundedness to Petri net theory and provide a sufficient condition for this property. Two applications are described: a rate synchronization network in manufacturing systems, to illustrate some of the Petri net results, and a machine with a priority based part servicing policy, which possesses Lagrange stability.
scientific article; zbMATH DE number 819187
scientific article