Laguerre-Gramian-based model order reduction of bilinear systems

In this paper, we propose a model order reduction algorithm based on low-rank Gramian approximation for bilinear systems. The main idea of the approach is to use approximate low-rank factors of the controllability and observability Gramians, which are constructed from the expansion coefficients of the matrix exponential functions in the space spanned by Laguerre functions using a recurrence formula, to generate approximate balanced system for the large-scale bilinear system. Then, the reduced-order model is obtained by truncating the states corresponding to the small approximate generalized Hankel singular values. Finally, a numerical experiment is provided to demonstrate the effectiveness of the proposed method.