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}}}}=\sum\limits_{{\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