  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.
