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Infinite-dimensional continuous-time linear systems: Stability and structure analysis

Infinite-dimensional continuous-time linear systems: Stability and structure analysis
Infinite-dimensional continuous-time linear systems: Stability and structure analysis

The question of exponential and asymptotic stability of infinite-dimensional continuous-time state-space systems is investigated. It is shown that every (par)balanced realization is asymptotically stable. Conditions are given for (par)balanced, input-normal, or output-normal realizations to be asymptotically and/or exponentially stable. The boundedness of the system operators is also studied. Examples of delay systems are given to illustrate the theory.

Balanced realizations, Hankel operators, Linear infinite-dimensional systems, Semigroups of operators, Stability
0363-0129
757-812
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Wu, Yuanyin
c25d67a2-c272-4fce-a8c5-90862020f181
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Wu, Yuanyin
c25d67a2-c272-4fce-a8c5-90862020f181

Ober, Raimund J. and Wu, Yuanyin (1996) Infinite-dimensional continuous-time linear systems: Stability and structure analysis. SIAM Journal on Control and Optimization, 34 (3), 757-812. (doi:10.1137/S0363012993245318).

Record type: Article

Abstract

The question of exponential and asymptotic stability of infinite-dimensional continuous-time state-space systems is investigated. It is shown that every (par)balanced realization is asymptotically stable. Conditions are given for (par)balanced, input-normal, or output-normal realizations to be asymptotically and/or exponentially stable. The boundedness of the system operators is also studied. Examples of delay systems are given to illustrate the theory.

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More information

Published date: 1996
Keywords: Balanced realizations, Hankel operators, Linear infinite-dimensional systems, Semigroups of operators, Stability

Identifiers

Local EPrints ID: 425010
URI: https://eprints.soton.ac.uk/id/eprint/425010
ISSN: 0363-0129
PURE UUID: 8a4566be-54b8-4b74-94ef-84096fde3f35
ORCID for Raimund J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

Catalogue record

Date deposited: 09 Oct 2018 16:30
Last modified: 14 Mar 2019 01:21

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Contributors

Author: Raimund J. Ober ORCID iD
Author: Yuanyin Wu

University divisions

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