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It is well known that an operator-valued function $\Theta$ from the Schurclass ${\bf S}(\mathfrak M,\mathfrak N)$, where $\mathfrak M$ and $\mathfrak N$are separable Hilbert spaces, can be realized as the transfer function of asimple conservative discrete time-invariant linear system. The knownrealizations involve the function $\Theta$ itself, the Hardy spaces or thereproducing kernel Hilbert spaces. On the other hand, as in the classicalscalar case, the Schur class operator-valued function is uniquely determined byits so called "Schur parameters". In this paper we construct simpleconservative realizations using the Schur parameters only. It turns out thatthe unitary operators corresponding to the systems take the form of fivediagonal block operator matrices, which are the analogs ofCantero--Moral--Vel\'azquez (CMV) matrices appeared recently in the theory ofscalar orthogonal polynomials on the unit circle. We obtain new models given bytruncated block operator CMV matrices for an arbitrary completely non-unitarycontraction. It is shown that the minimal unitary dilations of a contraction ina Hilbert space and the minimal Naimark dilations of a semi-spectral operatormeasure on the unit circle can also be expressed by means of block operator CMVmatrices.

Conservative discrete time-invariant systems and block operator CMV matrices