Order reduction of large scale second-order systems using Krylov subspace methods

In order reduction of large-scale linear time invariant systems, Krylov subspace methods based on moment matching are among the best choices today. However, in many technical fields, models typically consist of sets of second-order differential equations, and Krylov subspace methods cannot directly be applied. Two methods for solving this problem are presented in this paper: (1) an approach by Su and Craig is generalized and the number of matching moments is increased; (2) a new approach via first-order models is presented, resulting in an even higher number of matching moments. Both solutions preserve the specific structure of the second-order type model.