  Direct numerical simulation of dynamical systems is of fundamental importance
in studying a wide range of complex physical phenomena. However, the
ever-increasing need for accuracy leads to extremely large-scale dynamical
systems whose simulations impose huge computational demands. Model reduction
offers one remedy to this problem by producing simpler reduced models that are
both easier to analyze and faster to simulate while accurately replicating the
original behavior. Interpolatory model reduction methods have emerged as
effective candidates for very large-scale problems due to their ability to
produce high-fidelity (optimal in some cases) reduced models for linear and
bilinear dynamical systems with modest computational cost. In this paper, we
will briefly review the interpolation framework for model reduction and
describe a well studied flow control problem that requires model reduction of a
large scale system of differential algebraic equations. We show that
interpolatory model reduction produces a feedback control strategy that matches
the structure of much more expensive control design methodologies.
