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.