The Equation XR + QY = phi: A Characterization of Solutions,

In this paper we consider the solutions of the equation $XR + QY = \Phi $. Here Q , R , $\Phi $ are given $p \times q$, $m \times t$ and $p \times t$ polynomial matrices over a field k. X and Y are $p \times m$ and $q \times t$ polynomial matrices which are unknown. Using certain recent results on the realization of matrix fraction descriptions of transfer matrices, we give a characterization (parametrization) of all possible $(X,Y)$ which solve this equation. This also provides a system theoretic interpretation for this equation.