Recent results on output feedback problems

Given a real linear system ?? = (A,B,C) with m inputs, p outputs and degree n, we study the problem of generic pole placemmat by output feedback, which is to compute the constant C(m,p) such that the inequality C(m,p) ?? n is necessary and sufficient for generically positioning. the poles of the generic linear system by constant output feedback. In this note, we determine a constant C´ (m,p), which gives a sufficient condition for generic pole placement and which, to the best of the author´s knowledge, is at least as good an estimate of C(m,p) as any in the literature. In particular, we obtain Kimura´s first theorem [6a] and the recent result by Brockett and Byrnes [3] on pole assignability for the case mp = n as corollaries. We also announce some results on the construction of solutions in case mp= n, based on the degree formula of [3] and Galois theory. In particular, we answer a question, raised by Anderson, Bose, and Jury, on the existence of a rational procedure for computing the feedback law from the desired characteristic polynomial.