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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (10): 36-41.doi: 10.6040/j.issn.1671-9352.0.2016.492

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Banach空间上离散时间系统的多项式稳定

黄雷雷,宋晓秋*,卢威   

  1. 中国矿业大学数学学院, 江苏 徐州 221116
  • 收稿日期:2016-11-03 出版日期:2017-10-20 发布日期:2017-10-12
  • 通讯作者: 宋晓秋(1963— ),男,教授,研究方向为应用泛函分析,模糊数学相关理论与应用研究. E-mail:songxiaoqiu668@163.com E-mail:15262019085@163.com
  • 作者简介:黄雷雷(1991— ),女,硕士研究生,研究方向为泛函分析,演化方程解的渐近行为. E-mail:15262019085@163.com
  • 基金资助:
    国家自然科学基金资助项目(11371362)

On polynomial stability of linear discrete-time systems in Banach spaces

HUANG Lei-lei, SONG Xiao-qiu*, LU Wei   

  1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2016-11-03 Online:2017-10-20 Published:2017-10-12

摘要: 给出了Banach空间中有关多项式稳定的四种定义,借助实例阐释了四者的关系,利用指数型稳定性的研究方法,讨论了多项式稳定的离散特征,并得到了指数稳定理论中一些经典结论在多项式稳定情形下的变形。

关键词: 线性离散时间系统, 非一致多项式稳定, 一致多项式稳定, 多项式稳定, 强多项式稳定

Abstract: Four concepts of polynomial stability for difference equations are studied in Banach space. Characterizations of these concepts are given and the illustrative examples clarifies the relations between these concepts. Based on the extension of techniques for exponential stability to the case of polynomial stability, discrete characterizations of polynomial stability are discussed. The obtained results are generalizations of well-known theorems about the exponential stability.

Key words: nonuniform polynomial stability, strong polynomial stability, uniform polynomial stability, linear discrete-time systems, polynomial stability

中图分类号: 

  • O177.2
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