Dynamic pole assignment and Schubert calculus

The output feedback pole assignment problem is a classical problem in linear systems 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 $q(m + p - 1) + mp \geq n$. ©1996 Society for Industrial and Applied Mathematics