Model-order reduction of kth order MIMO dynamical systems using block kth order Krylov subspaces

Abstract

In this article, we study numerical methods for model-order reduction of large-scale kth order multi-input multi-output dynamical systems. We propose a new structure-preserving projection method, of which the projection subspace is a block kth order Krylov subspace based on a square matrix sequence and an initial rectangle matrix. A procedure, named as block kth order Arnoldi process, is presented for establishing an orthonormal basis of the projection subspace. Moreover, we show that the reduced system constructed by the new method has the same order of approximation as the standard block Krylov subspace method via linearization. Numerical experiments report the effectiveness of this method.

Keywords:

• high-order MIMO system
• block kth order Krylov subspace
• block kth order Arnoldi process
• model-order reduction
• moment

2000 AMS Subject Classifications :

• 65F30
• 65P99
• 93A15

Acknowledgements

The authors would like to thank the anonymous referees for their helpful suggestions, which greatly improved the article. Y. L. is supported by the National Natural Science Foundation of China under grant 10801048 and the Natural Science Foundation of Hunan Province under grant 09JJ6014. Y. W. is supported by the National Natural Science Foundation of China under grant 10871051, Shanghai Education Committee under grant 08SG01, Shanghai Science and Technology Committee under grant 08511501703, and 973 Program Project under grant 2010CB327900.