大系统渐近稳定的一般判别定理

GENERAL THEOREMS ON THE ASYMPTOTICAL STABILITY OF LARGE SCALE SYSTEMS

利用分解集结和向量 V 函数判别大系统的稳定性是一个广泛采用的有效方法.但过去一般限于集结成常系数线性比较方程,判定的只是指数稳定.本文提出一个非线性比较方程的构造定理,推广了 Bailey 方法,并且进一步推广了作者的前期工作,判定了大系统的非指数稳定.

A genedal theorem on the aggregation of a nonlinear comparison equation is proposed.A necessary and sufficient criterion for the asymptotical stability of the nonlinear comparison,equation in a more general form is obtained and two important corollaries are derived fromthat criterion.