  In this paper, we focus on model reduction of large-scale bilinear systems.
The main contributions are threefold. First, we introduce a new framework for
interpolatory model reduction of bilinear systems. In contrast to the existing
methods where interpolation is forced on some of the leading subsystem transfer
functions, the new framework shows how to enforce multipoint interpolation of
the underlying Volterra series. Then, we show that the first-order conditions
for optimal H2 model reduction of bilinear systems require multivariate Hermite
interpolation in terms of the new Volterra series interpolation framework; and
thus we extend the interpolation-based first-order necessary conditions for H2
optimality of LTI systems to the bilinear case. Finally, we show that
multipoint interpolation on the truncated Volterra series representation of a
bilinear system leads to an asymptotically optimal approach to H2 optimal model
reduction, leading to an efficient model reduction algorithm. Several numerical
examples illustrate the effectiveness of the proposed approach.
