Kybernetika 33 no. 4, 357-370, 1997

A geometric proof of Rosenbrock's theorem on pole assignment

Moisés Bonilla E., Jean-Jacques Loiseau and Rafael Baquero S.

Abstract:

A new proof of the famous Rosenbrock theorem on pole placement by static state feedback is given. This proof only uses well-known basic results of the geometric approach, that are the Brunovsk\'{y} canonical form of controllable systems and the splitting of the state space into cyclic subspaces relatively to the invariant factors of a linear map.

Classification:

93B55, 93B29, 93B27, 93B10