Dynamic pole assignment and schubert calculus

The output feedback pole assignment problem is a classical problem in linear theory. In this paper we calculate the number of complex dynamic compensators of order q assigning a given set of poles for a q-nondegenerate m-input, p-output system of McMillan degree n = q(m + p - 1) + mp. As a corollary it follows that when this number is odd, the generic system can be arbitrarily pole assigned by output feedback with a real dynamic compensator of order at most q if and only if q(m + p - 1) + mp ≥ n.