  Two comprehensive approaches are considered for constructing projection-based
reduced-order computational models for linear dynamical systems. The first one
reduces the governing equations written in the descriptor form, using a
Galerkin or Petrov-Galerkin projection onto a reduced-order basis or pair of
them, respectively. These bases can be constructed by any preferred method such
as the Proper Orthogonal Decomposition, Balanced Proper Orthogonal
Decomposition, or Moment Matching method. The second approach transforms first
the governing equations into their non-descriptor form before applying the same
projection-based model order reduction method. For several structural and
coupled fluid-structure dynamical systems, it is observed that the first
reduction approach leads to reduced-order models that exhibit significantly
better numerical stability and accuracy properties than those resulting from
the second one. These observations are reinforced by theoretical results that
anticipate and confirm the better stability properties obtained in general when
reducing the descriptor rather than non-descriptor form of the equations
governing a linear dynamical system.
