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在一些工程技术中,常需考虑非线性微分方程 dxi/(dt)=X_i(x_1, …, x_n) (i=1, 2, …, n) (1)过初值x_i(t_0)=0(i=1, 2, …,n)的运动稳定性问题[其中X_i(0,…,0)?0,i=1,2, …, n,即(1)的原点不为奇点]。由李雅普诺夫函数方法,从理论上可以解决这类问题,只要所找出的稳定域包含初值在内即可。但是在构成李雅普诺夫函数的过程中,当n逐渐增大(如n>10)时,其计算量是相当繁杂的。本文从理论上研究了以l组相互无关的微分方程组的李雅普诺夫函数
In some engineering techniques, the nonlinear differential equation dxi / (dt) = X_i (x_1, ..., x_n) (i = 1, 2, ..., n) (i = 1, 2, ..., n) [where X_i (0, ..., 0)? 0, i = 1,2, ..., n, that is the origin of (1) . By Lyapunov function method, in theory, this kind of problem can be solved, as long as the stable region is found to include the initial value. However, in the process of forming Lyapunov functions, the computation complexity is quite complicated when n is gradually increasing (for example, n> 10). In this paper, the Lyapunov function of a set of mutually independent differential equations is studied theoretically