On the computation and parametrization of proper denominator assigning compensators for strictly proper plants

Abstract

Given a right coprime MFD of a strictly proper plant P(s) = NR(s) DR(s)−1 with DR(s) column proper a simple numerical algorithm is derived for the computation of all polynomial solutions [XL(s), YL(s)] of the polynomial matrix Diophantine equation XL(s) DR(s) + YL(s) NR(s) = DC(s) which give rise to the class Φ (P, DC) of proper compensators C(s) ≔ XL(s)−1 YL(s) that when employed in a unity feedback loop, result in closed-loop systems S(P, C) with a desired denominator DC(s). The parametrization of the proper compensators C(s) ∈ Φ(P, DC) is obtained and the number of independent parameters in the parametrization is given.