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Asymptotic stability and Riesz basis property for tree-shaped network of strings
  • ISSN号：1009-6124
  • 期刊名称：系统科学与复杂性学报(英文版)
  • 时间：0
  • 页码：225-252
  • 语言：中文
  • 分类：O174.2[理学—数学;理学—基础数学] O175.13[理学—数学;理学—基础数学]
  • 作者机构：[1]College of Science, Civil Aviation University of China, Tianjin 300300, China, [2]Department of Mathematics, Tianjin University, Tianjin 300072, China
  • 相关基金：This research is supported in part by the Natural Science Foundation of China under Grant No. 60874035 and by the Scientific Research Initiation Foundation of Civil Aviation University of China （08QD09X）.
  • 相关项目：偏微分网络系统的控制
作者： Xu, Genqi|Guo, Yanni|
关键词： RIESZ基, 渐近稳定性, 树形网络, 字符串, 物业, 状态空间, 广义特征, 线性阻尼, Completeness, network of strings, riesz basis with parentheses, stability.
中文摘要：

这份报纸讨论 asymptotic 稳定性和 Riesz 基础产生因为颤动的一个一般塑造树的网络串。所有外面的顶点被假定被修理，内部顶点被强加线性抑制反馈。这份报纸证明系统由 C 0-semigroup 理论提出得好、 asymptotically 稳定。与一些另外的条件，系统的光谱被显示位于与想象的轴平行的脱衣，所有概括特徵函数的集合在州的空间被完成。这些导致有系统的概括特徵函数的一个序列的结论，它与括号形成一个 Riesz 基础州的空格。

英文摘要：

This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear damping feedbacks. This paper shows that the system is well-posed and asymptotically stable by C0-semigroup theory. With some additional conditions, the spectrum of the system is shown to be located in a strip that is parallel to the imaginary axis and the set of all generalized eigenfunctions is completed in the state space. These lead to the conclusion that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis with parenthesis for the state space.

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期刊信息
  • 《系统科学与复杂性学报：英文版》
  • 主管单位:中国科学院
  • 主办单位:中国科学院系统科学研究所
  • 主编：
  • 地址：北京东黄城根北街16号
  • 邮编：100080
  • 邮箱：
  • 电话：010-62541831 62541834
  • 国际标准刊号：ISSN：1009-6124
  • 国内统一刊号：ISSN：11-4543/O1
  • 邮发代号:82-545
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国工程索引,美国科学引文索引（扩展库）,英国科学文摘数据库
  • 被引量:125