针对单输入单输出(SISO)线性时不变系统,提出了Grassmann流形上基于交叉Gram矩阵的双侧H2最优模型降阶方法.首先,将误差系统的H2范数通过交叉Gram矩阵表示,并且把它看成关于变换矩阵的代价函数.其次,引入Grassmann流形,将代价函数看作是定义在Grassmann流形上的非负实值函数.然后,在Grassmann流形上进行线性搜索,寻找使得代价函数尽可能小的一组变换矩阵.运用此方法对大规模SISO线性时不变系统进行降阶,可以得到精度较高的降阶系统.最后,数值算例验证了该算法的近似效果.%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.
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