Nudelman interpolation, parametrizations of lossless functions and balanced realizations.

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

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