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In this paper, we consider model order reduction for bilinear systems withnon-zero initial conditions. We discuss choices of Gramians for both thehomogeneous and the inhomogeneous parts of the system individually and provehow these Gramians characterize the respective dominant subspaces of each ofthe two subsystems. Proposing different, not necessarily structure preserving,reduced order methods for each subsystem, we establish several strategies toreduce the dimension of the full system. For all these approaches, error boundsare shown depending on the truncated Hankel singular values of the subsystems.Besides the error analysis, stability is discussed. In particular, a focus ison a new criterion for the homogeneous subsystem guaranteeing the existence ofthe associated Gramians and an asymptotically stable realization of the system.

Model order reduction for bilinear systems with non-zero initial states -- different approaches with error bounds