Darlington realization of matrix-valued functions

For matrix-valued functions $s(z)$ of Schur class (holomorphic and contractive in the circle $|z|<1$) the author considers the Darlington realization and isolates the set $S\Pi$ of those $s(z)$ for which this realization is possible. For the case in which $s(z)\in S\Pi$ satisfies the condition $I-s^*(\zeta)s(\zeta)>0$, a description is obtained of all Darlington realizations of $s(z)$ and the minimum realizations are isolated.