Invariance of asymptotic stability of perturbed linear systems on Hilbert space
type: Item
instance of: scholarly article
title: Invariance of asymptotic stability of perturbed linear systems on Hilbert space
zbMATH Open document ID: 0697.93051
DOI: 10.1007/BF00939936
author: P. Li
author: N. U. Ahmed
published in: Journal of Optimization Theory and Applications
publication date: 1991-01-01T00:00:00Z
review text: The questions of stabilizability of structurally perturbed (or uncertain) linear systems in Hilbert space of the form \(\dot x=(A+P(r))x+Bu\) are considered. The operator A is assumed to be the infinitesimal generator of a \(C_ 0\)-semigroup of contractions T(t), \(t\geq 0\), in a Hilbert space X; B is a bounded linear operator from another Hilbert space U to X; and \(\{\) P(r), \(r\in \Omega \}\) is a family of bounded or unbounded perturbations of A in X, where \(\Omega\) is an arbitrary set, not necessarily carrying any topology. Sufficient conditions are presented that guarantee controllability and stabilizability of the perturbed system, given that the unperturbed system \(\dot x=Ax+Bu\) has similar properties. In particular, it is shown that, for certain classes of perturbations, weak and strong stabilizability properties are preserved for the same state feedback operator.
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 4143887
zbMATH Keywords: stabilizability
zbMATH Keywords: semigroup
zbMATH Keywords: perturbations
zbMATH Keywords: feedback
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00939936
OpenAlex ID: W1967643437
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description: scientific article; zbMATH DE number 4143887