Lagrange stability and boundedness of discrete event systems
type: Item
instance of: scholarly article
title: Lagrange stability and boundedness of discrete event systems
zbMATH Open document ID: 0849.93051
DOI: 10.1007/BF01439154
author: Kevin M. Passino
author: Kevin L. Burgess
author: Anthony N. Michel
published in: Discrete Event Dynamic Systems
publication date: 1996-11-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 68Q45
Mathematics Subject Classification ID: 68Q85
zbMATH DE Number: 819187
zbMATH Keywords: logical discrete event system
zbMATH Keywords: stability
zbMATH Keywords: Petri net
zbMATH Keywords: Lyapunov function
zbMATH Keywords: uniform ultimate boundedness
zbMATH Keywords: manufacturing systems
zbMATH Keywords: Lagrange stability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 819187