关于时滞差分系统稳定性和有界性的一些推广

Extentions on Stability and Boundedness in Delay Difference Systems

基于泛函微分方程的部分变元的稳定性和有界性，对有限时滞差分系统定义了关于部分变元的稳定性和有界性等概念．藉助比较原理，建立了利用离散的李雅普诺夫泛函或李雅普诺夫函数判别解的稳定性或有界性的准则．从而推广了已有的相应结果，并丰富了时滞差分系统定性理论的内容．

Inspired by the concepts of stability and boundedness with respect to partial components for the functional differential equations in the relevant literature, this paper defined the concepts of stability and boundedness with respect to partial components for finite delay difference systems. By means of the comparison principles it establised several criteria on stability as well as boundedness of solutions via discrete Liapunov functionals or Liapunov functions, which extended the relevant known results and enriched the contents of the qualitative theory for delay difference systems.