  In this paper, the connections are investigated between two different
approaches towards the parametrization of multivariable stable all-pass systems
in discrete-time. The first approach involves the tangential Schur algorithm,
which employs linear fractional transformations. It stems from the theory of
reproducing kernel Hilbert spaces and enables the direct construction of
overlapping local parametrizations using Schur parameters and interpolation
points. The second approach proceeds in terms of state-space realizations. In
the scalar case, a balanced canonical form exists that can also be parametrized
by Schur parameters. This canonical form can be constructed recursively, using
unitary matrix operations. Here, this procedure is generalized to the
multivariable case by establishing the connections with the first approach. It
gives rise to balanced realizations and overlapping canonical forms directly in
terms of the parameters used in the tangential Schur algorithm.
