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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Vydané v:	Linear algebra and its applications Ročník 434; číslo 5; s. 1325 - 1335
Hlavní autori:	Beitia, M.A., Compta, A., Hoyos, I., Peña, M.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier Inc 01.03.2011 Elsevier
Predmet:	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
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Popis
Shrnutí:	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