  In this paper, we consider the structure-preserving model order reduction
problem for multi-input/multi-output bilinear control systems by tangential
interpolation. We propose a new type of tangential interpolation problem for
structured bilinear systems, for which we develop a new structure-preserving
interpolation framework. This new framework extends and generalizes different
formulations of tangential interpolation for bilinear systems from the
literature and also provides a unifying framework. We then derive explicit
conditions on the projection spaces to enforce tangential interpolation in
different settings, including conditions for tangential Hermite interpolation.
The analysis is illustrated by means of three numerical examples.

Numerical Analysis;Numerical Analysis;Systems and Control;Systems and Control;Dynamical Systems;Optimization and Control