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Versal deformations of bilinear systems under output-injection equivalence
García Planas, María Isabel
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Bilinear systems under output injection equivalence are considered. The aim of this paper is to study what happens when a slight perturbation affects the coeffi- cients of the matrices defining a bilinear equation in C n . For this goal we will use the Arnold’s techniques, that is to say we will construct a versal deformation of a differentiable family of bilinear systems which are the orthogonal linear varieties to the orbits of output injec- tion equivalent bilinear systems. Versal deformations provide a special parametrization of bilinear systems space, which can be applied to perturbation analysis and investigation of complicated objects like singular- ities and bifurcations in multi-parameter bilinear sys- tems
Àrees temàtiques de la UPC::Matemàtiques i estadística
Bilinear systems
versal deformations
equivalence relation
output injection.
Sistemes dinàmics diferenciables
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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