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Issue ESAIM: Proc.
Volume 20, 2007
RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005
Page(s) 83 - 92
DOI http://dx.doi.org/10.1051/proc:072008
Published online 13 October 2007

ESAIM: Proc., 2007, Vol. 20, pp. 83-92
DOI: 10.1051/proc:072008

Calculating the $H_{\infty}$-norm of large sparse systems via Chandrasekhar iterations and extrapolation

Younes Chahlaoui1, Kyle A. Gallivan1 and Paul Van Dooren2

1  SCS, Florida State University, Tallahassee FL 32306-4120, USA
2  CESAME, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium;

younes.chahlaoui@laposte.net
gallivan@csit.fsu.edu
vdooren@csam.ucl.ac.be

(Published online: 13 October 2007)

Abstract
We describe an algorithm for estimating the $\mathcal{H}_{\infty}$-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm uses Chandrasekhar iterations to obtain an estimate of the $\mathcal{H}_{\infty}$-norm and then uses extrapolation to improve these estimates.


Résumé
Nous décrivons un algorithme pour estimer la norme $\mathcal{H}_{\infty}$ d'un système dynamique linéaire à temps invariant de grande dimension décrit par un modèle d'espace d'état discret. L'algorithme emploie des récurrences de Chandrasekhar pour obtenir une estimation de la norme $\mathcal{H}_{\infty}$ puis emploie l'extrapolation pour améliorer ces estimations.


Key words: $\mathcal{H}_{\infty}$-norm, large sparse systems, Chandrasekhar iterations.


© EDP Sciences, ESAIM 2007


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