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Realizations of perturbations of an observable pair with prescribed indices
Beitia, M.A.; Compta Creus, Albert; de Hoyos, Inmaculada; Peña Carrera, Marta
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Observable pairs
Perturbations of a system
Versal deformations
Canonical form
Àlgebra lineal
Classificació AMS::37 Dynamical systems and ergodic theory::37A Ergodic theory
Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
Article
Elsevier
         

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