  We investigate the parametrization issue for discrete-time stable all-pass
multivariable systems by means of a Schur algorithm involving a Nudelman
interpolation condition. A recursive construction of balanced realizations is
associated with it, that possesses a very good numerical behavior. Several
atlases of charts or families of local parametrizations are presented and for
each atlas a chart selection strategy is proposed. The last one can be viewed
as a nice mutual encoding property of lossless functions and turns out to be
very efficient. These parametrizations allow for solving optimization problems
within the fields of system identification and optimal control.
