VERSAL DEFORMATIONS OF BILINEAR SYSTEMS
UNDER OUTPUT-INJECTION EQUIVALENCE
M. Isabel Garcia-Planas
Bilinear systems under output injection equivalence are considered. The aim of this paper is to study what happens when a slight perturbation affects the
coefficients of the matrices defining a bilinear equation in $\mathbb{C}^{n}$. 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 injection 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 singularities and bifurcations in
multi-parameter bilinear systems.