Routh-Hurwitz判别法的一个应用

Application of Routh-Hurwitz criterion

Ｒｏｕｔｈ－Ｈｕｒｗｉｔｚ判别定理在理论上和工程应用中有着广泛的应用。但由于在实际应用中，往往会出现临界情形，即Ｒ－Ｈ条件中的某些严格不等式不能满足，而较弱的不严格能够成立。本文针对此问题给出了特征多项式的一些零点处于临界状态的所谓半稳定时的一种判别方法，这种方法弥补了Ｒ－Ｈ定理的应用局限性，在理论上和实际应用上是简单方便的，可以看成为Ｒ－Ｈ定理的补充。

Routh-Hurwitz criterion of polynomials plays an important role in both theory and application of linear systems. But sometimes its conditions are too strong to be satisfied. A weaker form criterion is given in this paper, which generalizes the Routh-Hurwitz criterion of stable polynomials. It gives a necessary and sufficient condition for a real polinomial to have non-positive real part eigenvalues. The criterion needs only to calculate determinants. It is easy to know the number of eigenvalus which have zero real parts and negative real parts and, of course, the number of zero eigenvalues, if the polynomial is semi-stable.