Parametrising the solutions of the generalised partial realisation problem through an atlas of coordinates

Given a finite nice sequence of matrices ℒ and a positive integer d, the set of generalised partial realisations of ℒ of order d is a stratified smooth manifold. An atlas of coordinate charts for each stratum is provided that locally parametrises it. In particular, the set of all generalised partial...

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Bibliographic Details
Published in:International journal of control 2013-01, Vol.86 (1), p.54-69
Main Authors: Baragaña, I., Puerta, F., Zaballa, I.
Format: Article
Language:English
Subjects:
atlas of coordinates
brunovsky indices
Charts
Integers
Manifolds
Mathematical analysis
Matrices
Matrix methods
parametrisation
partial realisation
reduced form
smooth manifold
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Summary:Given a finite nice sequence of matrices ℒ and a positive integer d, the set of generalised partial realisations of ℒ of order d is a stratified smooth manifold. An atlas of coordinate charts for each stratum is provided that locally parametrises it. In particular, the set of all generalised partial realisations of order d of any given nice sequence ℒ will be described.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2012.717724