Model Reduction via Truncated Cross-Gramian for Bilinear Systems

Abstract

In this work, we present a new cross-gramian. The proposed gramian is a truncated gramian which supports bilinear systems. It is proven that the truncated cross-gramian can be obtained by solving ordinary Sylvester equation. It is computationally less expensive to compute the truncated cross-gramian compared to the standard cross-gramians which are solutions to the generalized Sylvester equations. A projection based model reduction method is proposed based upon the truncated crossgramian. The proposed method is among the first cross-gramian based methods - if not the only one- which is developed for bilinear systems. This model reduction is computationally more efficient than model reduction techniques which are derived from standard gramains or the truncated controllability and observability gramians.