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Overlapping block-balanced canonical forms for various classes of linear systems

Overlapping block-balanced canonical forms for various classes of linear systems
Overlapping block-balanced canonical forms for various classes of linear systems

Through the use of balanced realizations it has been possible to derive parametrizations and canonical forms for various classes of minimal linear systems of given dimension. A possible problem of these parametrizations is that they are not overlapping. This could be a drawback for the application of balanced parametrizations in such areas as system identification, model reduction and optimization. It is the topic of this paper to derive overlapping parametrizations which are closely related to the existing balanced parametrizations. We first introduce input-normal canonical forms which are defined through a novel way of choosing nice selections of columns of the reachability matrix. These canonical forms provide overlapping parametrizations in the sense that they form a real analytic atlas of the manifold of systems which are considered. Then we introduce so-called block-balanced input normal forms which use the previously constructed input normal forms as building blocks. The classes of systems for which such parametrizations are given are the stable minimal systems, positive-real minimal systems, bounded-real minimal systems and the class of all minimal systems of given McMillan degree. The results include both the single-input single-output and the multivariable case. In the single-input single-output case, however, the issue of choosing nice selections of columns does not occur. Therefore in this case the derivation and presentation of the results is considerably simplified.

0024-3795
171-225
Hanzon, Bernard
ec8a3e31-d488-4a69-8318-6ff08024dd7c
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36
Hanzon, Bernard
ec8a3e31-d488-4a69-8318-6ff08024dd7c
Ober, Raimund J.
31f4d47f-fb49-44f5-8ff6-87fc4aff3d36

Hanzon, Bernard and Ober, Raimund J. (1998) Overlapping block-balanced canonical forms for various classes of linear systems. Linear Algebra and Its Applications, 281 (1-3), 171-225. (doi:10.1016/S0024-3795(98)10056-3).

Record type: Article

Abstract

Through the use of balanced realizations it has been possible to derive parametrizations and canonical forms for various classes of minimal linear systems of given dimension. A possible problem of these parametrizations is that they are not overlapping. This could be a drawback for the application of balanced parametrizations in such areas as system identification, model reduction and optimization. It is the topic of this paper to derive overlapping parametrizations which are closely related to the existing balanced parametrizations. We first introduce input-normal canonical forms which are defined through a novel way of choosing nice selections of columns of the reachability matrix. These canonical forms provide overlapping parametrizations in the sense that they form a real analytic atlas of the manifold of systems which are considered. Then we introduce so-called block-balanced input normal forms which use the previously constructed input normal forms as building blocks. The classes of systems for which such parametrizations are given are the stable minimal systems, positive-real minimal systems, bounded-real minimal systems and the class of all minimal systems of given McMillan degree. The results include both the single-input single-output and the multivariable case. In the single-input single-output case, however, the issue of choosing nice selections of columns does not occur. Therefore in this case the derivation and presentation of the results is considerably simplified.

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More information

Accepted/In Press date: 9 March 1998
Published date: 15 September 1998

Identifiers

Local EPrints ID: 425017
URI: https://eprints.soton.ac.uk/id/eprint/425017
ISSN: 0024-3795
PURE UUID: 6ccd6a93-d83c-4384-b093-2be65c4f8ffb
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: 14 Mar 2019 01:21

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Contributors

Author: Bernard Hanzon
Author: Raimund J. Ober ORCID iD

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