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Completely J-positive linear systems of finite order

Completely J-positive linear systems of finite order
Completely J-positive linear systems of finite order

Completely J-positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J-positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J-symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J-symmetric realizations are discussed.

Asymptotic stability, Completely J-positive linear system of finite order, Defining measure, Definitizable operator, Discrete time linear system, Kreǐn space, Realization theory, Sign symmetry, Spectral minimality
0025-584X
75-101
Gheondea, Aurelian
97dd2d38-c290-4cd8-9f95-b580a9501f8b
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Gheondea, Aurelian
97dd2d38-c290-4cd8-9f95-b580a9501f8b
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Gheondea, Aurelian and Ober, Raimund J. (1999) Completely J-positive linear systems of finite order. Mathematische Nachrichten, 203 (1), 75-101. (doi:10.1002/mana.1999.3212030105).

Record type: Article

Abstract

Completely J-positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J-positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J-symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J-symmetric realizations are discussed.

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More information

Published date: 1999
Keywords: Asymptotic stability, Completely J-positive linear system of finite order, Defining measure, Definitizable operator, Discrete time linear system, Kreǐn space, Realization theory, Sign symmetry, Spectral minimality

Identifiers

Local EPrints ID: 425022
URI: http://eprints.soton.ac.uk/id/eprint/425022
ISSN: 0025-584X
PURE UUID: de3f8a86-8591-4397-b7fa-e0e02dac7b2a
ORCID for Raimund J. Ober: ORCID iD orcid.org/0000-0002-1290-7430

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Date deposited: 09 Oct 2018 16:30
Last modified: 06 Jun 2024 02:04

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Contributors

Author: Aurelian Gheondea
Author: Raimund J. Ober ORCID iD

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