Arbitrary Pole Shifting via Decentralized Static Output Feedback

Abstract

In this paper the problem of arbitrary pole placement via constant decentralized output feedback is studied for minimal systems described by a proper transfer function matrix P(s) ε Rmxp (s), (m = ∑ mi and p = ∑ pi), with McMillan degree n. The method presented here is based on asymptotic linearization around a decentralized degenerate compensator, of the pole placement map related to the problem. The solution is given in closed form in terms of a one parameter, (ε), family of constant decentralized controllers, for which the closed loop poles approach the required ones as e tends to zero. It is shown that the method works generically when m'• p > n where m' = min {mi, i=1 ,…, k).