Riesz Basis Property and Stability of Planar Networks of Controlled Strings

被引：12

作者：

Han, Zhong Jie ^{[1
]}

Wang, Lei ^{[1
]}

机构：

[1] Tianjin Univ, Dept Automat, Tianjin 300072, Peoples R China

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 02期

关键词：

Star-shaped network; Spectrum; Root vector; Riesz basis; Stability; TREE-SHAPED NETWORKS; VIBRATING STRINGS; CONTROLLABILITY; STABILIZATION; BEAMS;

D O I：

10.1007/s10440-009-9459-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the basis property of root vectors of a star-shaped networks of strings whose exterior ends are clamped and common node has a damping. The main operator determined by the networks is non-normal. By the asymptotical technique, we show that its spectra distribute in a strip parallel to the imaginary axis, and there is a sequence of root vectors (generalized eigenvectors and eigenvectors) that forms a Riesz basis with parentheses for the Hilbert state space. As a application of this result, we discuss the stability of the system.

引用

页码：511 / 533

页数：23

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