On structured perturbations for two classes of linear infinite-dimensional systems
type: Item
instance of: scholarly article
title: On structured perturbations for two classes of linear infinite-dimensional systems
zbMATH Open document ID: 0856.93050
DOI: 10.1007/BF02169488
author: Stuart Townley
author: Zbigniew Emirsjlow
author: A. J. Pritchard
published in: Dynamics and Control
publication date: 1996-09-18T00:00:00Z
review text: The authors investigate two classes of infinite-dimensional systems described by an abstract differential equation \(\dot x=(A+B\Delta C)x\) on a Hilbert space, where \(A\), \(B\) and \(C\) are linear, possible unbounded operators and \(\Delta\) is an unknown, linear, bounded perturbation. The two classes are defined in terms of the properties imposed on the triple \((A,B,C)\). It is shown that for every \(\Delta\) the perturbed system given by \((A+E\Delta F,B,C)\) inherits all the properties of the unperturbed system \((A,B,C)\) if \((A,E,F)\) and \((A,B,C)\) are in the same class. The results in this paper can be considered as generalizations of results of \textit{R. F. Curtain}, \textit{H. Logemann}, \textit{S. Townley}, and \textit{H. Zwart} [J. Math. Syst. Estim. Control 4, 493-496 (1994; Zbl 0815.93046)]. However, the theory is less general than the perturbation theory developed for regular systems by \textit{G. Weiss} [Math. Control Signals Syst. 7, 23-57 (1994; Zbl 0819.93034)]. Since the classes of systems considered in this paper are strictly smaller than the class of regular systems, the invariance results in this paper are more specific than those by Weiss [loc. cit.].
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 911965
zbMATH Keywords: infinite-dimensional systems
zbMATH Keywords: unbounded operators
zbMATH Keywords: perturbation
zbMATH Keywords: invariance results
Wikidata QID: Q57920000
reviewed by: H. Logemann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 911965