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

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 [X L (s), YL (s)] of the polynomial matrix Diophantine equation X L (s)DR(s)+YL (s)NR(s) = DC (s) which give rise to the class Φ(P, DC ) of proper compensators C(s) := X L (s)−1YL (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.