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

Kouki Mohamed, Abbes Mehdi, Mami Abdelkader

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

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v59i0.9622



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.