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### 基于交叉Gram矩阵低秩分解的非对称线性系统的模型降阶

1. 长江大学信息与数学学院, 荆州 434023
• 出版日期:2018-04-25 发布日期:2021-06-25

WANG Wen, WANG Yue, WANG Wenhui , XIAO Zhihua. Model Order Reduction Based on Low-Rank Decomposition of the Cross Gramian for Non-Symmetric Linear Systems[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 926-938.

### Model Order Reduction Based on Low-Rank Decomposition of the Cross Gramian for Non-Symmetric Linear Systems

WANG Wen, WANG Yue, WANG Wenhui ,XIAO Zhihua

1. School of Information and Mathematics, Yangtze University, Jingzhou 434023
• Online:2018-04-25 Published:2021-06-25

For non-symmetric linear systems, a model order reduction based on low-rank decomposition of the cross Gramian is proposed. The proposed approach first expands the impulse responses of the original system and its dual system in the space spanned by Legendre polynomials, and then the low-rank factors of the cross Gramian are directly constructed from the expansion coefficients by the orthogonality. After that, an approximate balanced system of the original system is obtained by projection transformation. Then, the reduced-order model is obtained by truncating the states corresponding to the small approximate Hankel singular values under the given tolerance of the approximation error. The method is flexible, efficient and adaptive. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
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