高维非线性自治系统的全局稳定和不稳定性

本文用一般分离变量型v函数,证明了一般高维非线性自治微分方程组解的全局稳定性和不稳定性的定理,将基本结果用于n维分离变量的非线性自治系统,改进和包含了文献1,2]的结果,且得到其他一些结果,对n维Lurè型直接控制系统,给出了在Hurwitz角域0,∞)内绝对稳定的简便实用判据。

ON GLOBAL STABILITY AND INSTABILITY OF SOLUTIONS TO THE NON-LINEAR AUTONOMOUS SYSTEM OF HIGHER DIMENSION

In this paper, a general V function with separating variables is used to prove thetheorems on the global asymptotic stability and instability of solutions to the general non-linear autonomous system of differential eqations of any dimension. This basic result is applied to non-linear systems with separating variables, and generalizes and includes the known results in papers 1] and 2]. The result is also applied to the divect eontrol system of the n-th order Luré type, and two criterion, for the absolute stability in the Hurwitz angle region 0. ∞], which are easy to be applied have been proved. Moreover, some other new results are proved too.