一类四阶非线性系统的李雅普诺夫函数构造和零解稳定性

Construction of Liapunov's Function and Stabitiility of the Fourth-order Nonliear System

计算出了四阶常系数线性系统的各种形式的李雅普诺夫函数,并将四阶非线性系统化成它的等价系统,通过类比的方法构造出一类四阶非线性系统的李雅普诺夫函数,从而获得该系统零解全局渐近稳定的充分条件.

We calculate some kinds of Liapunov＇s functions of the fourth-order linear system with constant coefieients and converte the fourth-order nonlinear system into their equivalence systems and their liapunov＇s functions by the use of ＂comparison method＂. Thereby we derive the sufficient conditions of the global stability of the nonlinear systems.