A differential representation for multivariable linear systems with disturbances

It is shown how to compute a differential representation for a multivariable linear system with disturbances
\dot{x}(t)=Ax(t)+Bu(t)+ W_{x}w(t)
y(t)=Cx(t)+ Eu(t)+ W_{y}w(t)
. Explicit formulas for
M_{y}(D)
and
M_{z}(D)
in a differential equivalent representation
P(D)z(t)=u(t)+M_{z}(D)w(t)
y(t)=R(D)z(t)+M_{y}(D)w(t)
are presented in this paper.