Abstract
A standard approach to reduced-order modeling of higher-order linear dynamical
systems is to rewrite the system as an equivalent first-order system and then employ
Krylov-subspace techniques for reduced-order modeling of first-order systems. While this
approach results in reduced-order models that are characterized as Pade-type or even true
Pade approximants of the system's transfer function, in general, these models do not
preserve the form of the original higher-order system. In this paper, we present a new
approach to reduced-order modeling of higher-order systems based on projections onto
suitably partitioned Krylov basis matrices that are obtained by applying Krylov-subspace
techniques to an equivalent first-order system. We show that the resulting reduced-order
models preserve the form of the original higher-order system. While the resulting
reduced-order models are no longer optimal in the Pade sense, we show that they still
satisfy a Pade-type approximation property. We also introduce the notion of Hermitian
higher-order linear dynamical systems, and we establish an enhanced Pade-type approximation
property in the Hermitian case.
