系统等价在二维系统研究中发挥重要作用, 它与二元多项式矩阵等价问题密切相关. 文章主要研究几类二元多项式矩阵与其Smith型等价问题, 得到一些新的结果及这几类矩阵分别与其Smith型等价的判别准则. 这些准则可以通过计算给定多项式矩阵的低一阶子式生成理想的Gr\"{o}bner基进行检验.

The equivalence of systems plays an important role in 2D systems, which is closely related to the equivalence of bivariate polynomial matrices. In this paper, the Smith forms of several classes of bivariate polynomial matrices are investigated. Some new results and criteria on the equivalence of these matrices are obtained. These criteria are easily checked by computing the reduced Gr\"{o}bner basis of the ideal generated by the minors of lower order of the given matrix.