一类非线性自治大系统的全局稳定性

本文研究非线性自治大系统
$frac{{{rm{d}}{{rm{x}}_{rm{i}}}}}{{{rm{dt}}}}=sumlimits_{{rm{i}}=1}^{rm{r}} {{{rm{f}}_{{rm{ij}}}}({rm{xj}})({rm{i}}=1,ldots,{rm{r}})} $
这里,x_i∈Rⁿⁱ,f_ij∈C(R^nj,Rⁿⁱ,f_ij(o)=0,得到保证其零解为全局一致渐近稳定的充分条件(见定理1)。

On Uniformly Asymptotic Stability in the Large to the Non-Linear Autonomous Large-Scale Systems

Let f_ij (i,j=1,2……,r) are continuous,the autonomous nom-lineararge-scale system with equatiom
$frac{{{rm{d}}{{rm{x}}_{rm{i}}}}}{{{rm{dt}}}}=sumlimits_{{rm{i}}=1}^{rm{r}} {{{rm{f}}_{{rm{ij}}}}({rm{xj}})({rm{i}}=1,ldots,{rm{r}})} $
are considered,where X_i is n_i vectors and,assume it has a null solution. Some rather well conditions,under which the null solution of above system is uniformly asymptotically stable in the large,is obtained