A new proof of Rosenbrock's theorem on pole assignment

Abstract

A new constructive proof is given of a theorem by Rosenbrock on changing the poles of a finite-dimensional linear time-invariant dynamical system by linear constant state feedback. The necessity of Rosenbrock's conditions is proven by a geometrical argument. The sufficiency of these conditions is established by means of a recursion to construct feedbacks. The algorithms for the recursion are proven in this paper, and the author has implemented the algorithms with computer programs.