Proper rational matrix diophantine equations and the exact model matching problem

Relying on the theory behind the Smith-MacMillan form of a rational matrix at
s = \infty
, a necessary and sufficient condition is derived from the solvability of matrix Diophantine equations of the form
A(s)X(s)+B(s)Y(s) = M(s)
, where
A(s), B(s)
, and
M(s)
are given proper rational matrices and
X(s)
and
Y(s)
are unknown proper rational matrices. It is shown that the above result can be used in order to resolve in a new illuminating way the exact model matching problem (EMMP). If a solution to EMMP exists, then the family of all solutions is parametrized.