将实数域上线性系统能控性PBH判据推广到多元有理函数域$F(z)$.由于实数域是$F(z)$的子域, 且为结构化矩阵,一次多项式矩阵和混合矩阵都可视为一类$F(z)$上矩阵,所以获得的判据适用的范围更广. 给出了几个应用实例.

In this paper, the PBH criterion of controllability for  linear systems over the real field is extend to the systems over the  rational function field $F(z)$. Since the real field is a subfield  of $F(z)$ and SM  (structured matrix), one-degree polynomial matrix and mixed matrix can  be considered to be a class of matrices over $F(z)$, the criterion  obtained in this paper is more universal. Finally some examples are given.