一類非線性自治大系統的全局穩定性

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

摘要: 本文研究非線性自治大系統
\frac\rmd\rmx_\rmi\rmdt=\sum\limits_\rmi=1^\rmr \rmf_\rmij(\rmxj)(\rmi=1, \ldots,\rmr)
這里,x_i∈Rⁿⁱ,f_ij∈C(R^nj,Rⁿⁱ,f_ij(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 f_ij (i, j=1, 2……, r) are continuous, the autonomous nom-lineararge-scale system with equatiom
\frac\rmd\rmx_\rmi\rmdt=\sum\limits_\rmi=1^\rmr \rmf_\rmij(\rmxj)(\rmi=1, \ldots,\rmr)
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