Realizations of perturbations of an observable pair with prescribed indices

It is well known that, when a full rank observable pair (C,A) is slightly perturbed, the new observability indices k′ are majorized by the initial ones k, k≻k′. Conversely, any indices k′ majorized by k can be obtained by perturbing (C,A). The aim of this paper is the explicit construction of pertur...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 434; no. 5; pp. 1325 - 1335
Main Authors: Beitia, M.A., Compta, A., Hoyos, I., Peña, M.
Format: Journal Article Publication
Language:English
Published: Amsterdam Elsevier Inc 01.03.2011
Elsevier
Subjects:
37 Dynamical systems and ergodic theory
37A Ergodic theory
93 Systems Theory; Control
93B Controllability, observability, and system structure
Algebra
Canonical form
Classificació AMS
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Matemàtiques i estadística
Mathematics
Observable pairs
Perturbations of a system
Sciences and techniques of general use
Versal deformations
Àlgebra lineal
Àrees temàtiques de la UPC
37A20
Observable pairs
15A21
Perturbations of a system
Versal deformations
93B10
93C73
Canonical form
Observability
ISSN:0024-3795
Online Access:Get full text
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Summary:It is well known that, when a full rank observable pair (C,A) is slightly perturbed, the new observability indices k′ are majorized by the initial ones k, k≻k′. Conversely, any indices k′ majorized by k can be obtained by perturbing (C,A). The aim of this paper is the explicit construction of perturbations of (C,A) which have the desired indices k′ by means of a sequence of uniparametrical versal perturbations. Even more, using versal deformations we refine this construction in such a way that the perturbation has the maximum possible number of zeros and no parameters in the square part.
ISSN:0024-3795
DOI:10.1016/j.laa.2010.11.009