多元多项式矩阵等价的进一步结果

doi:10.12341/jssms21407

系统科学与数学 ›› 2021, Vol. 41 ›› Issue (12): 3299-3310.DOI: 10.12341/jssms21407

多元多项式矩阵等价的进一步结果

李冬梅, 桂盈盈

湖南科技大学数学与计算科学学院, 湘潭 411201

收稿日期:2021-07-24 修回日期:2021-10-23 出版日期:2021-12-25 发布日期:2022-03-16
基金资助:
国家自然科学基金（11871207）资助课题.

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李冬梅, 桂盈盈. 多元多项式矩阵等价的进一步结果[J]. 系统科学与数学, 2021, 41(12): 3299-3310.

LI Dongmei, GUI Yingying. Further Results on the Equivalence of Multivariate Polynomial Matrices[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(12): 3299-3310.

Further Results on the Equivalence of Multivariate Polynomial Matrices

LI Dongmei, GUI Yingying

School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201

Received:2021-07-24 Revised:2021-10-23 Online:2021-12-25 Published:2022-03-16

多维系统常用多项式矩阵来描述，系统理论中的多维系统等价问题也常被转化为多项式矩阵等价问题进行研究.文章主要研究两类多元多项式矩阵的等价问题，得到这些矩阵分别与其Smith型等价的判别条件.这些条件的检验是比较容易实现的，文章中也通过具体的等价实例进行说明.

关键词： 多维系统, 多项式矩阵, 矩阵等价, Smith型

Multidimensional systems are often described by polynomial matrices, and problems on the equivalence of multidimensional systems in system theory are often transformed into problems on the equivalence of polynomial matrices. In this paper, we mainly study the equivalence of two kinds of multivariate polynomial matrices, and obtain the discriminant conditions for the equivalence of these matrices and their Smith forms, respectively. The conditions are easily verified, and an example is also used to illustrate these in the paper.

Key words: Multidimensional systems, polynomial matrices, the equivalence of matrices, Smith form

MR(2010)主题分类:

15A21
15A23

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