一类三阶非线性微分方程的全局渐近稳定性

Global Asymptotic Stability of a Class of Third-Order Nonlinear Differential Equation

对一类三阶非线性微分方程利用能量度量法构造了较好的Lyapunov函数,得到其零解全局渐近稳定的一组充分条件,而且去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统正半轨有界,所得结果包含并改进了旧的结果.

A better Lyapunov function of a class of third-order nonlinear differential equations has been constructed by the method of the energy metric algorithm, and some sufficient conditions of globally asympotic stability of zero solution are obtained. The hard condition that Lyapunov function shoud be infinite has been removed, and the only requirement is that the positive orbit of the equation should be bounded. The result not only covers but also improves some of the old results.