H ₂ optimal model order reduction of the discrete system on the product manifold

This paper studies the H ₂ optimal model order reduction of the discrete system based on the cross Gramian, which equips both the controllability and observability information. The cross Gramian is first employed to obtain the H ₂ norm of the discrete systems. Then, the constrained conditions of the H ₂ optimal model order reduction problem of the discrete systems are relaxed, and a new H ₂ optimal model order reduction problem on the product manifold is reformulated. Finally, geometry of the resultant optimization problem is investigated and an iterative algorithm is presented. The efficiency of the proposed algorithm is demonstrated by a practical example.