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inria-00546743, version 1

Nudelman interpolation, parametrizations of lossless functions and balanced realizations.

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

Automatica 43 (2007) 1329-1338

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.

  • a –  CMA - Ecole des Mines de Paris
  • 1:  Centre de Mathématiques Appliquées (CMA)
  • MINES ParisTech - École nationale supérieure des mines de Paris
  • 2:  APICS (INRIA Sophia Antipolis)
  • INRIA
  • Domain : Mathematics/Optimization and Control
  • Keywords : Parametrization – Inner matrices – Interpolation algorithms – Scattering parameters – Differential geometric methods – Discrete-time systems – Multivariables systems.
 
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  • From: Martine Olivi <>
  • Submitted on: Wednesday, 15 December 2010 13:55:24
  • Updated on: Wednesday, 15 December 2010 14:55:32