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Overlapping block-balanced canonical forms and parametrizations: The stable siso case

Overlapping block-balanced canonical forms and parametrizations: The stable siso case
Overlapping block-balanced canonical forms and parametrizations: The stable siso case

The balanced canonical form and parametrization of Ober for the case of SISO stable systems are extended to block-balanced canonical forms and related input-normal forms and parametrizations. They form an overlapping atlas of parametrizations of the manifold of stable SISO systems of given order. This extends the usefulness of these parametrizations, e.g., in gradient algorithms for system identification. As an implication of our construction it follows that each of the subsets of the parametrization of [R. Ober, Internat. J. Control, 46 (1987), pp. 643-670] corresponding to a choice for the structural indices is in fact an imbedded submanifold of the manifold of stable SISO systems of fixed order.

Atlas, Canonical forms, Differentiable manifolds, Linear dynamical systems, Stable systems, System identification
0363-0129
228-242
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. (1997) Overlapping block-balanced canonical forms and parametrizations: The stable siso case. SIAM Journal on Control and Optimization, 35 (1), 228-242. (doi:10.1137/S0363012993260549).

Record type: Article

Abstract

The balanced canonical form and parametrization of Ober for the case of SISO stable systems are extended to block-balanced canonical forms and related input-normal forms and parametrizations. They form an overlapping atlas of parametrizations of the manifold of stable SISO systems of given order. This extends the usefulness of these parametrizations, e.g., in gradient algorithms for system identification. As an implication of our construction it follows that each of the subsets of the parametrization of [R. Ober, Internat. J. Control, 46 (1987), pp. 643-670] corresponding to a choice for the structural indices is in fact an imbedded submanifold of the manifold of stable SISO systems of fixed order.

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More information

Published date: 1997
Keywords: Atlas, Canonical forms, Differentiable manifolds, Linear dynamical systems, Stable systems, System identification

Identifiers

Local EPrints ID: 425015
URI: https://eprints.soton.ac.uk/id/eprint/425015
ISSN: 0363-0129
PURE UUID: 0871fe73-7b67-497a-b6be-2dbcb61e2fb1
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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