一类非线性三阶系统的全局渐近稳定性

Globally Asymptotic Stability Analysis of a Class of Nonlinear Third-order Systems

针对非线性三阶系统x…+g(.x)x¨+f(x,.x).x+h(x)=p(x,.x,x¨)构造出了一个适当的Lyapunov函数,并且去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界,所得结果改进了相关文献的结论.最后,文中给出了例子仿真说明充分条件的有效性.

For the nonlinear third order system x^…＋g（x^.）x^..＋f（x,x^.）x^.＋h（x）=p（x,^x.,^x..）, a better Lyapunov function is constructed in this paper, and the original stronger requirement is removed here as the Lyapunov function must trend to infinity, and there is only one need that the positive half orbit of the system is bounded. The results improve the conclusions of relevant literature. At last, the simulation of example shows the conditions for the effectiveness.