改进Liapunov稳定性基本定理中Ⅴ函数的条件

在常微分方程稳定性理论中,Liapunov稳定性基本定理中的V函数是一个定号函数,且它关于时间t的全导数dV/dt的正负号要求与V相反。本文论述了在零点稳定及一致稳定性的两个充分性定理。从而表明Liapunov稳定性基本定理中的V函数的正定性,可用在一同心闭曲线簇上的正定的V函数来代替,因此V可为变号函数。

IMPROVEMENT OF CONDITION OF V-FUNCTION IN LIAPUNOV FUNDAMENTAL THEOREM OF STABILITY

In the stability theory of ordinary differential equations, the V-function of Liapunov fundamental theorem of stability is a fixed sign and its total derivative is contrary sign to V-fuction. In this paper, we have discussed the two sufficient theorems-of stability and uniform stability in zero point, which shows that the positive definite V-fuction on the variety of concentric closed curves is used instead of positive definite V-fuction of Liapunov fundamental theorem of stability, and then V-function may well be the function of signed numbers.