Nudelman interpolation, parametrizations of lossless functions and balanced realizations.

Jean-Paul Marmorat (1) , Martine Olivi (2)

1 CMA - Centre de Mathématiques Appliquées
2 APICS - Analysis and Problems of Inverse type in Control and Signal processing

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.

Mots clés: Multivariables systems.; Multivariables systems; Parametrization; Inner matrices; Interpolation algorithms; Scattering parameters; Differential geometric methods; Discrete-time systems

Domaines: Optimisation et contrôle [math.OC]

Jean-Paul Marmorat, Martine Olivi. Nudelman interpolation, parametrizations of lossless functions and balanced realizations.. Automatica, 2007, 43, pp.1329-1338. ⟨10.1016/j.automatica.2007.01.020⟩. ⟨inria-00546743⟩