Model reduction by moment matching, steady-state response and projections

The model reduction problem by moment matching for linear systems is revisited and connections between projection based methods and the notion of steady-state response are established. A systems theoretic interpretation of the (oblique) projectors used in Krylov methods is derived and a new family of reduced order models achieving moment matching is given. Finally, the equivalence between various families of reduced order models, all achieving moment matching, is established.