H₂ optimal model order reduction on the Stiefel manifold for the MIMO discrete system by the cross Gramian

In this paper, the H₂ optimal model order reduction method for the large-scale multiple-input multiple-output (MIMO) discrete system is investigated. First, the MIMO discrete system is resolved into a number of single-input single-output (SISO) subsystems, and the H₂ norm of the original MIMO discrete system is expressed by the cross Gramian of each subsystem. Then, the retraction and the vector transport on the Stiefel manifold are introduced, and the geometric conjugate gradient model order reduction method is proposed. The reduced system of the original MIMO discrete system is generated by using the proposed method. Finally, two numerical examples show the efficiency of the proposed method.