Irreducibility of dynamical equation realizations of sets of differential equations

The irreducibilities of dynamical equation realizations of sets of linear time-invariant differential equations
D(p)y(t) = N(p)u(t)
are studied. It is demonstrated that a realization of
D(p)y(t) = N(p)u(t)
can be irreducible only if the degree of the determinant of
D(s)
is equal to the degree of the rational matrix
D^{-1}(s)N(s)
.