两类三阶非线性系统零解的全局渐近稳定性

Globally Asymptotic Stability of Two Classes of Third-order Nonlinear Systems

对三阶非线性系统x+g(x,)+f(x,)+h(x)=0和…x+g(x,)+f(x,)+h(x)=p(x,,)构造出了较好的Lyapunov函数,得到其零解全局渐近稳定的充分性准则.去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界,所得结果包含并改进了原有的结果.

For two classes of third order nonlinear systems x ＋ g（ x ,x ） x ＋ f（ x ,x ） ＋ h （ x ） = 0 and x ＋ g（ x ,x ） x＋ f（ x,x） ＋ h （ x ） = p（ x ,x ,x）, the better Lyapunov functions are constructed in this paper. By using these functions, some new sufficient conditions for globally asymptotic stability are obtained. Tile present results include and improve some old ones, since the original stronger requirement is removed here that the Lyapunov fimction must trend to infinity, and there is only one need that the positive half orbit of the system is bounded.