The University of Southampton
University of Southampton Institutional Repository

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.

Full text not available from this repository.

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

Catalogue record

Date deposited: 09 Oct 2018 16:30
Last modified: 07 Oct 2020 02:22

Export record

Altmetrics

Contributors

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

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×