Miniversal deformations of bilinear systems
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 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.
CYBERNETICS AND PHYSICS, Vol. 2, No. 2. 2013 , 84-89.