On the general problem of pole assignment

Abstract

Given a linear, time-invariant, minimal and strictly proper system  set of monic polynomials φ _i (s), i = l, 2, [tdot],q, such that φ _i (s) divides φ _i−1 (s), i = 2, 3, [tdot],q a method for finding a proper feedback system  which makes the invariant polynomials of the closed-loop system equal to the φ _i (s) is established and a sufficient condition which ensures the existence of  is determined. This method can also be used to assign the poles of the compensated system provided that certain poles are multiple. The order of the required compensator is generally loss than that of the Luenberger or the Wolovich compensation schemes.