Miniversal deformations of bilinear systems
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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
CitationGarcia-Planas, M.I. Miniversal deformations of bilinear systems. "Cybernetics and physics", 2013, vol. 2, núm. 2, p. 84-89.