关于三阶线性时变系统的稳定性的一点注记

The Asymptotic Stability of the Trivial Solution of Third-Order Nonautonmous Linear Systems

本文应用分解系统的方法[1 ,2 ] 讨论了三阶线性时变系统dx dt=A(t)x平凡解的稳定性 .放弃了系数矩阵A(t)的特征值均有负实部的要求 ,给出了保证该系统零解渐近稳定的充分条件 .

In this paper we discuss the stability of the trivial solution of the third_order nonautonomous linear system d x /d t=A(t)x by utilizing the method of decomposing systems [1,2] .Giving up the demand that au the eigenvalues of A(t) have negative real part,this paper is devoted to presenting sufficient conditions of guaranteeing the asymptotic stability of the zero solution x(t)≡0 of the system.