Reduction of Second Order Systems using Second Order Krylov subspaces

Authors:	Lohmann Boris, Technical University of Munich, Germany Salimbahrami Behnam, Technical University of Munich, Germany
Topic:	1.1 Modelling, Identification & Signal Processing
Session:	Model Reduction Techniques
Keywords:	Model reduction, Second-order systems, Large scale systems, Reduced-order models

Abstract

By introducing the second order Krylov subspace, a method for the reduction of second order systems is proposed leading to a reduced system of the same structure. This generalization of Krylov subspace involves two matrices and some starting vectors and the reduced order model is found by applying a projection directly to the second order model without any conversion to state space. A numerical algorithm called second order Arnoldi is used to calculate the projection matrix and some of the first moment of the reduced and original systems match. A sufficient condition for stability of the reduced model is given and finally, the method is applied to an electrostatically actuated beam.