多元多项式矩阵等价的进一步结果  

Further Results on the Equivalence of Multivariate Polynomial Matrices

作　　者：李冬梅[1] 桂盈盈 LI Dongmei;GUI Yingying(School of Mathematics and Computing Sciences,Hunan University of Science and Technology,Xiangtan 411201)

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭411201

出　　处：《系统科学与数学》2021年第12期3299-3310,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11871207)资助课题。

摘　　要：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.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.

关 键 词：多维系统 多项式矩阵 矩阵等价 Smith型 

分 类 号：O151.21[理学—数学]