On the perturbation of bimodal control linear systems

The aim of this paper is the study of local perturbations of a bimodal system which consists of two linear control systems on each side of a given hyperplane. We follow Arnold’s technique based on obtaining a miniversal deformation corresponding to the action of a group associated to a simultaneous feedback equivalence. An application to the study of the controllability of local perturbations of such a system is included.