关于运用Liapunov函数的滞后型系统部分稳定性的注释

A Note on the Partial Stability of Retarded System Using Liapunov Functions

中文关键词:  滞后型泛函微分方程  解  稳定性

英文关键词:retarded functional differential equation  solution  stability

中文摘要:

      本文给出了泛函微分方程部分稳定性的一些条件. 这些条件是运用Liapunov函数判定泛函微分方程的一致稳定性和一致渐近稳定性. 这些部分稳定性的条件发展了泛函微分方程一致稳定性和一致渐近稳定性的Razumikhin定理. 给出了证实这些结果的实例. 通过实例进一步说明了这些新的部分稳定性的条件.

英文摘要:

      Sufficient conditions for the stability with respect to part of the functional differential equation variables are given. These conditions utilize Lyapunov functions to determine the uniform stability and uniform asymptotic stability of functional differential equations. These conditions for the partial stability develop the Razumikhin theorems on uniform stability and uniform asymptotic stability of functional differential equations. An example is presented which demonstrates these results and gives insight into the new stability conditions.