Bifurcation diagrams for feedback families of linear systems (Q1080401)

An application of V. I. Arnold's method of versal deformation to linear control systems is discussed. The first half of the paper exposes some results of \textit{V. V. Udilov} [Kibern. Vychisl. Tekh. 47, 10-25 (1980; Zbl 0461.93017)] concerning the full feedback action on the space of reachable pairs (A,B) with m input and n state variables, rk B\(=m\). In particular, a miniversal deformation of a system \((A_ 0,B_ 0)\) in Brunovsky canonical form is described. In the second part of the note a result concerning the bifurcation diagram of a generic family of control pairs is presented which is a consequence of Udilov's theorem.