Exact controllability and complete stabilizability for linear systems in Hilbert spaces
type: Item
instance of: scholarly article
title: Exact controllability and complete stabilizability for linear systems in Hilbert spaces
zbMATH Open document ID: 0888.93010
DOI: 10.1016/S0893-9659(96)00107-3
author: J. Karrakchou
author: R. Rabah
published in: Applied Mathematics Letters
publication date: 1997-01-01T00:00:00Z
review text: Linear, stationary, infinite-dimensional continuous-time control systems defined in Hilbert spaces are considered. Using methods of functional analysis, necessary and sufficient conditions for exact controllability in finite time are formulated and proved. Next, the relationships between exact controllability and complete stabilizability are discussed. It is shown, that with minimal assumptions concerning the semigroup generated by system operator, complete stabilizability implies exact controllability. Moreover, many remarks and comments on exact controllability and complete stabilizability are given. Similar exact controllability problems have been considered in the paper [\textit{J. C. Louis} and \textit{D. Wexler}, J. Differ. Equ. 49, 258-269 (1983; Zbl 0505.49018)].
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 1078532
zbMATH Keywords: infinite-dimensional control systems
zbMATH Keywords: exact controllability
zbMATH Keywords: complete stabilizability
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
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full work available at URL: s0893-9659(96)00107-3
OpenAlex ID: W2041465959
description: scientific article; zbMATH DE number 1078532