A constructive proof of Gibson's stability theorem
type: Item
instance of: scholarly article
title: A constructive proof of Gibson's stability theorem
zbMATH Open document ID: 1287.47033
author: Fatiha Alabau-Boussouira
author: Piermarco Cannarsa
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2013-03-14T00:00:00Z
review text: It was proved in [\textit{J. S. Gibson}, SIAM J. Control Optimization 18, 311--316 (1980; Zbl 0434.93044)] that, if the infinitesimal generator of an exponentially stable \(C_0\)-semigroup is additively perturbed by a compact operator, then the resulting semigroup is again exponentially stable, provided that it is strongly stable. The present paper gives another proof of this result. The authors' proof is constructive, provides a natural extension from a Hilbert to a Banach setting, and weakens slightly the compactness perturbation assumption. Applications are also discussed.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 6144735
zbMATH Keywords: \(C_0\)-semigroups
zbMATH Keywords: exponential stability
zbMATH Keywords: compact perturbation
reviewed by: Carlos S. Kubrusly
MaRDI profile type: Publication
full work available at URL: dcdss.2013.6.611
OpenAlex ID: W2005159059
DOI: 10.3934/DCDSS.2013.6.611
description: scientific article; zbMATH DE number 6144735