Eigenvalue assignment by dynamic output feedback: a new sufficiency criterion in the real case

In this paper we give a rank condition which guarantees the arbitrary pole assignability of a given system by dynamic compensators of degree at most q. By using this rank condition we establish a new strong sufficiency condition which ensures the arbitrary pole assignability of the generic system. Our proof also comes with a concrete numerical procedure to construct a particular compensator which assigns a given set of closed loop poles.