一类四阶时滞微分方程的渐进稳定性

Asymptotic stability of a certain fourth-order delay differential equation

能否作出合适的Lyapunov函数是研究非线性时滞系统稳定性的关键,通过类比的方法构造Lyapunov函数.研究一类四阶时滞微分方程,通过构造方程的零解渐近稳定的充分性条件,结合零解是一致稳定的充分条件,得到方程的零解渐近稳定的充分性准则.

By analogy to Lyapunov function,whether or not an appropriate Lyapunov function can be constructed is the key to the study of the stability of nonlinear time-delay system.A class of fourth-order differential equation is studied.By constructing sufficient conditions of the asymptotic stability of zero solution of equation,the adequate criteria of the asymptotic stability of zero solution of equation is obtained.