基于离散时间系统交叉Gram矩阵的H₂最优模型降阶方法

H₂ Optimal Model Order Reduction Method Based on the Cross-Gramian for Discrete-Time Systems

针对单输入单输出(SISO)离散时间系统,本文提出了基于交叉Gram矩阵的一阶必要条件。首先,应用交叉Gram矩阵,得到误差系统的H2范数;然后,根据交叉Gram矩阵所满足的Sylvester方程,得到了误差系统H2范数关于降阶系统系数矩阵的梯度;最后,根据误差系统H2范数的梯度,得到了基于交叉Gram矩阵的一阶必要条件。与此同时,得到降阶系统。

In this paper, the first-order necessary conditions based on the cross-Gramian are presented for the discrete-time Single-Input-Single-Output (SISO) systems. First, by using the cross-Gramian, the H2-norm of the error system is obtained. Then, according to the Sylvester equations satisfied by the cross-Gramian, the gradients are obtained with respect to the coefficient matrices of the reduced order system. Finally, due to the gradients of the H2-norm of the error system, the first-order necessary conditions based on the cross-Gramian are achieved. Meanwhile, the reduced order system is accordingly obtained.