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ASYMPTOTIC STABILITY AND RIESZ BASIS PROPERTY FOR TREE-SHAPED NETWORK OF STRINGS 被引量：1

ASYMPTOTIC STABILITY AND RIESZ BASIS PROPERTY FOR TREE-SHAPED NETWORK OF STRINGS
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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.
作者 YanniGUO Genqi XU
机构地区 College of Science Department of Mathematics
出处 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第2期225-252,共28页 系统科学与复杂性学报（英文版）
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）.
关键词 COMPLETENESS network of strings riesz basis with parentheses stability. 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
分类号 O174.2 [理学—基础数学] O175.13 [理学—基础数学]
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参考文献26

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引证文献1

Journal of Systems Science & Complexity
2011年 第2期

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