一类三阶非线性时滞系统的全局渐近稳定性

运用类比法构造Lyapunov函数,讨论了一类三阶非线性时滞系统的稳定性,给出了其零解全局渐近稳定的充分性准则.在证明过程中,去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统的正半轨线有界,对于正半轨线的有界性是利用了类似构造Poincare-Bendix-son环域外边界的方法来判定.最后,给出了一些具有一般意义的三阶非线性系统推广而成的时滞系统的全局渐近稳定的结果.

Global asymptotic stability of a class of third-order nonlinear delay system

By using the method of analogy to construct Lyapunov function,the stability of a class of third-order nonlinear delay system is discussed and some sufficient conditions of global asymptotical stability of its zero solution are obtained.In the proof,the condition that generally required for Lyapunov function to be infinite is removed;only the positive orbit of the system to be bounded is demanded,which is determined by the similar method to construct the outside boundary of Poincare-Bendixson annular region.Finally,some results of the global stability of the nonlinear delay system extended by some universal third-order nonlinear system are presented.