关于一类非驻定系统的稳定性

ON THE STABILITY OF A KIND OF NON-STATIONARY SYSTEMS

本文在常值矩阵 A=(a_(ij))以零为 r 重特征根,其余根均有负实部条件下讨论了非驻定系统 dx/dt=sum.from to j=1(a_(ij)x_j+f_i(t,x_1,…,x_n))零解的稳定问题,得到了判断该系零解为稳定或不稳定的充分条件。

This paper discusses the stability of Non-stationary System dx_1/dt +f_1(t,x_1,…,x_n) under the conditions that the characteristic equation of costant matrix A=(a_(ij)) has r-multiple zero roots and its rest roots posses nagtive real parts.Sufficient conditions that can judge the trivial solution of the discussed system to be stable or not are obtained.