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An iterative model order reduction method for large-scale dynamical systems. (English) Zbl 1373.93073

Summary: 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.

MSC:

93B11 System structure simplification
93A15 Large-scale systems
93C05 Linear systems in control theory
65F15 Numerical computation of eigenvalues and eigenvectors of matrices

Software:

benchmodred
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Full Text: DOI

References:

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