巴尔巴欣一克拉索夫斯基全局稳定性定理的一个注记

A Remark on Barbashin—Krasovski's Global Stability Theorem

巴尔巴欣—克拉索夫斯基全局稳定性定理要求V(x)是无限大正定函数,本文采用具有性质(A)的正定函数V(x)放宽了这个要求,从而V(x)可以是有界函数。

In this paper, the global stability theorem by E.A. Barbashin-N.N. Krasovski is extended by a substitution of a positive definite function with property (A) for the unbounded positive definite function. Thus, V(x) can be a bounded function.