关于多项式稳定的若干注记

Some Notes on Polynomial Stability

在多项式稳定性经典理论中,通常利用双线性变换将多项式的Schur稳定性的判定转化为变换后多项式Hurwitz稳定性的判定.文章首先指出了双线性变换的缺陷,同时给出了一个替代变换;其次引进了一个判定多项式Hurwitz稳定性的充要条件。

In classic polynomial stability theory, determining Schur stability of f（z） can be translated into observing the Hurwitz stability for f（（w＋1）/（w-1））（w-1）^n through a bilinear transformation. In this paper, some notes are taken for the purpose of identifying the weaknesses found in the commonly used bilinear transformation, in which a substitute transform is proposed, and consequently a necessary and sufficient condition is introduced.