Model reduction by moment matching does not
preserve, in a systematic way, the transient response of the
system to be reduced, thus limiting the use of this model
reduction technique in control problems. With the final goal
of designing reduced-order models which can effectively be
used (not just for analysis but also) for control purposes, we
determine, using a data-driven approach, an estimate of the
moments and of the transient response of an unknown system.
We compute the unique, up to a change of coordinates, reducedorder
model which possesses the estimated transient and,
simultaneously, achieves moment matching at the prescribed
interpolation points. The error between the output of the system
and the output of the reduced-order model is minimized and
we show that the resulting system is a constrained optimal (in
a sense to be specified) reduced-order model. The results of the
paper are illustrated by means of a simple numerical example.