摘要
本文对著名的Routh-Hurwitz稳定性判据作了补充证明(对特征多项式含偶次因子时的特殊处理的证明),从而比原判据提供了更多的内容:不仅可以确定特征多项式中位于开右半S平面的零点数,而且能确定位于开左半S平面的零点和虚轴上的零点数,还能确定虚零点的重数.全部证明所用数学工具仅限于复平面上的幅角计算,较为简明.
This paper presents an supplementary proof of the well-known Routh-Hurwitz stability criterion, when characteristic polynomial contains even degree factor. It presents more content than former criterion. It can determine not only the number of open right half- plane zeros of the characteristic polynomial, but also the number of open left half-plane zeros and the number of the jω-axis zeros. Further, it can determine the multiplicities m, of the zeros on the jω-axis. Complete proof requires only elementary geometric considerations in the complex plane, that is more simple.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
1993年第1期21-30,共10页
Journal of Southeast University：Natural Science Edition
关键词
稳定性判据
特征多项式
R-H判据
Routh-Hurwitz criterion, stability criteria, characteristic polynomials
