微分差分方程解的渐近稳定性

The Critcrions of Asymptotic Stability of A Class of Differential-Difference Equations

本文不同于文[1-5]的方法,从另外的角度研究了一类非线性微分差分方程零解的渐近稳定性,得到了充分条件.另外,本文考虑了特征方程具有零根的时变线性微分差分方程平凡解的渐近稳定性,得到了渐近稳定的充分条件,从而说明了对于时变线性微分差分系统,其特征方程根均具有负实部不是系统平凡解渐近稳定的必要条件。

In this paper, we use the method which is different from the papers [1-5] to study the asymptotic stability of a class of nonlinear differential-difference equations and give the criterions of asymptotic stability of the systems. Morever, we use the method to study the time-varying linear differential-difference equations and give an example to have shown that it is not the necessary condition of the asympototic stability of the zero solution of time-varying linear DDE that every eigenvalue of time-varying linear DDE has negative real part.