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AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

Published online by Cambridge University Press:  05 April 2017

K. MOHAMED ,
A. MEHDI  and
M. ABDELKADER
K. MOHAMED*
Affiliation:
Université de Tunis El Manar, École Nationale d’Ingenieurs de Tunis, Laboratoire de Recherche Analyse et Commande des Systèmes, LR-11-ES20, BP 37, Le Belvedere 1002 Tunis, Tunisia email [email protected]
A. MEHDI
Affiliation:
Université de Carthage, École Nationale d’Ingénieurs de Carthage, Laboratoire de Recherche Analyse et Commande des Systèmes, LR-11-ES20, BP 37, Le Belvedere 1002 Tunis, Tunisia email [email protected]
M. ABDELKADER
Affiliation:
Université de Tunis El Manar, Faculté des Sciences de Tunis, Laboratoire de Recherche Analyse et Commande des Systèmes, LR-11-ES20, BP 37, Le Belvedere 1002 Tunis, Tunisia email [email protected]
*
✉[email protected]
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Abstract

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We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$ and $H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

Keywords

model order reductionAORASVDGramianlarge scaleKrylovmoment matchingH∞
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 1 , July 2017 , pp. 115 - 133
Copyright
© 2017 Australian Mathematical Society 

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