ABSTRACT 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.

中文翻译：

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基于交叉 Gramian 的 MIMO 离散系统 Stiefel 流形 H2 最优模型降阶

摘要 本文研究了大规模多输入多输出 (MIMO) 离散系统的 H2 最优模型降阶方法。首先，将MIMO离散系统分解为若干个单输入单输出(SISO)子系统，原始MIMO离散系统的H2范数用各子系统的交叉Gramian表示。然后，引入了Stiefel流形上的回缩和向量传输，提出了几何共轭梯度模型降阶方法。利用所提出的方法生成原始MIMO离散系统的简化系统。最后，两个数值例子表明了所提出方法的有效性。