Partial stability and boundedness of general dynamical systems on metric spaces
type: Item
instance of: scholarly article
title: Partial stability and boundedness of general dynamical systems on metric spaces
zbMATH Open document ID: 1035.37008
DOI: 10.1016/S0362-546X(02)00167-0
author: Anthony N. Michel
author: Alexander Molchanov
author: Ye Sun
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The authors develop a comparison theory for the partial stability of invariant sets and for the boundedness of motions for dynamical systems on metric spaces. To accomplish this, they utilize mappings from the dynamical system under study to a well understood comparison system which preserve the stability and boundedness properties. The results are applicable to a wide class of dynamical systems including some systems that cannot be determined by classical differential equations or inequalities. Moreover, the results are not only applicable to the analysis of equilibria but also to invariant sets. The theory is applied to the analysis of a class of discrete event systems, in particular, a computer network load balancing problem.
reviewed by: Norbert Koksch
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1880009
zbMATH Keywords: vector Lyapunov function
zbMATH Keywords: stability
zbMATH Keywords: asymptotic stability
zbMATH Keywords: partial stability
zbMATH Keywords: exponential stability
zbMATH Keywords: invariant set
zbMATH Keywords: boundedness of motions
zbMATH Keywords: stability preserving mappings
zbMATH Keywords: dynamical system
zbMATH Keywords: discrete event system
zbMATH Keywords: comparison system
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00167-0
OpenAlex ID: W2040601125
description: scientific article; zbMATH DE number 1880009