Geodesic
Darlington realization of matrix-valued functions
Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1295-1326.

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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. 
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D. Z. Arov. Darlington realization of matrix-valued functions. Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1295-1326. http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a5/

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