H2 order-reduction for bilinear systems based on Grassmann manifold

In this paper, we focus on optimal H2 model reduction methods for bilinear systems. The optimal H2 model reduction problem can be viewed as a minimization problem on Grassmann manifold. By utilizing the geometry of Grassmann manifold, a gradient descent model reduction algorithm and a conjugate gradient model reduction algorithm based on Grassmann manifold are given. These two algorithms can simulate well the behavior of the original system and the order-reduced systems generated by our algorithms can satisfy the minimal stability requirement. Numerical examples are given to illustrate the effectiveness of our methods.