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Algorithmes numériques pour les matrices polynomiales avec applications en commande

Juan Carlos Zuniga Anaya 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : In this thesis we develop new numerical algorithms for polynomial matrices. We tackle the problem of computing the eigenstructure (rank, null-space, finite and infinite structures) of a polynomial matrix and we apply the obtained results to the matrix polynomial J-spectral factorization problem. We also present some applications of these algorithms in control theory. All the new algorithms presented here are based on the computation of the constant null-spaces of block Toeplitz matrices associated to the analysed polynomial matrix. For computing these null-spaces we apply standard numerical linear algebra methods such as the singular value decomposition or the QR factorization. We also study the application of fast methods like the generalized Schur method for structured matrices. We analyze the presented algorithms in terms of algorithmic complexity and numerical stability, and we present some comparisons with others algorithms existing in the literature.
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Contributor : Emilie Marchand <>
Submitted on : Tuesday, November 8, 2005 - 2:03:12 PM
Last modification on : Thursday, June 10, 2021 - 3:02:31 AM
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  • HAL Id : tel-00010911, version 1


Juan Carlos Zuniga Anaya. Algorithmes numériques pour les matrices polynomiales avec applications en commande. Mathématiques [math]. INSA de Toulouse, 2005. Français. ⟨tel-00010911⟩



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