A numerical method for the computation 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 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 to 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.