一类微分方程组的解对部分变元的Ляпунов稳定性

LYAPUNOV'S PARTIAL STABILITY OF A CLASS DIFFERENTIAL EQUATIONS

本文应用纯量Ляпунов函数方法及Ляпунов向量函数方法,讨论了一类微分方程组零解的部分变元稳定性,给出了零解对部分变元浙近稳定及全局新近稳定的判定定理。

In this paper, Lyapunov's partial stability of the solutions of system(1) is discussed. Using the methods of scalar Lyapunov function and vector Lyapunov function, We obtain the conditions under which the solution x=0 of Eq.(1) is globally asymptotically stable about partial variables (x_1, …,x_m), Finally, using the method above, we discuss Lyapunov's partial stability of a more general class of differential equation.