An iterative model order reduction method for large-scale dynamical systems

Authors

  • Kouki Mohamed Universit´e de Tunis El Manar, ´ Ecole Nationale d’Ingenieurs de Tunis, Laboratoire de Recherche Analyse et Commande des Syst`emes.
  • Abbes Mehdi Universit´e de Carthage, ´ Ecole Nationale d’Ing´enieurs de Carthage, Laboratoire de Recherche Analyse et Commande des Syst`eme
  • Mami Abdelkader Universit´e de Tunis El Manar, Facult´e des Sciences de Tunis, Laboratoire de Recherche Analyse et Commande des Syst`emes

DOI:

https://doi.org/10.21914/anziamj.v59i0.9622

Keywords:

AORA, SVD, Gramian, large scale, Krylov, moment matching, \(H_{\infty}\).

Abstract

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. doi:10.1017/S1446181117000049

Published

2017-09-05

Issue

Vol. 59 (2017)

Section

Articles for Printed Issues