Strong stability of quasi-affine transforms of contraction semigroups and the steady-state Riccati equation
type: Item
instance of: scholarly article
title: Strong stability of quasi-affine transforms of contraction semigroups and the steady-state Riccati equation
zbMATH Open document ID: 0545.93057
DOI: 10.1007/BF00938443
published in: Journal of Optimization Theory and Applications
publication date: 1985-01-01T00:00:00Z
review text: This paper studies strong stability of the class of strongly continuous Hilbert space semigroups which are quasi-affine transforms of contraction semigroups. Sufficient conditions for such a semigroup to be approximately strong stable are given. Application to the stabilizability problem of Hilbert space semigroups, using a feedback involving a solution of the steady-state Riccati equation are made. Our key tool is the generalization of the \textit{J. P. LaSalle} [J. Differ. Equations 4, 57-65 (1968; Zbl 0159.120)] invariance principle by \textit{J. K. Hale} [J. Math. Anal. Appl. 26, 39-59 (1969; Zbl 0179.133)].
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 3869179
zbMATH Keywords: strong stability
zbMATH Keywords: quasi-affine transforms of contraction semigroups
zbMATH Keywords: steady-state Riccati equation
author: Nhan Levan
MaRDI profile type: Publication
cites work: Q3909518
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description: scientific article; zbMATH DE number 3869179