Aiming at the single input and single output (SISO) linear time-invariant system, we propose a two-sided H2 optimal model order reduction method based on the cross Gramian and Grassmann manifold. Firstly, the H2 norm of the error system is expressed by the cross Gramian, which is regarded as the cost function of transformation matrices. Secondly, by introducing the Grassmann manifold, the cost function is viewed as a nonnegative real function defined on the Grassmann manifold. Thirdly, we perform the linear-search method on the Grassmann manifold to seek a couple of transformation matrices, which makes the cost function as small as possible. We apply this method to an SISO linear time-invariant system and obtain a more accurate reduced order system. Numerical examples verify the effective approximation of the proposed method.

 

model order reduction, H2 optimality, cross gramian matrix, Grassmann manifold