Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Solving schubert problems with Littlewood-Richardson homotopies
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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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 $q(m+p-1)+mp\geq n$.