On Uniformly Asymptotic Stability in the Large to the Non-Linear Autonomous Large-Scale Systems
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摘要: 本文研究非線性自治大系統
$\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}})} $
這里,xi∈Rni,fij∈C(Rnj,Rni,fij(o)=0,得到保證其零解為全局一致漸近穩定的充分條件(見定理1)。Abstract: Let fij (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 Xi is ni 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-
Key words:
- non-linear system /
- autonomous system /
- large-scale system /
- stability in the large
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