  We propose an adaptive moment-matching framework for model order reduction of
quadratic-bilinear descriptor systems. In this framework, an important issue is
the selection of those shift frequencies where moment-matching is to be
achieved. Often, the choice is random or linked to the linear part of the
nonlinear system. In this paper, we extend the use of an existing a posteriori
error bound for general linear time invariant systems to quadratic-bilinear
systems and develop a greedy-type framework to select a good choice of
interpolation points for the construction of the projection matrices. The
results are compared with standard quadratic-bilinear projection methods and we
observe that the approximations obtained by the proposed method yield high
accuracy.
