Robustness with respect to small delays for exponential stability of abstract differential equations in Banach spaces

被引：2

作者：

Guo, FM ^{[1
]}

Tang, B

Huang, FL

机构：

[1] Univ Elect Sci & Technol China, Sch Appl Math, Chengdu 610054, Peoples R China

[2] Univ Elect Sci & Technol China, Sch Elect Engn, Chengdu 610054, Peoples R China

[3] Sichuan Univ, Math Coll, Chengdu 610064, Peoples R China

来源：

ANZIAM JOURNAL | 2006年 / 47卷

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

small delay; robust stability; fundamental operator;

D O I：

10.1017/S1446181100010130

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with robustness with respect to small delays for the exponential stability of abstract differential equations in Banach spaces. Some necessary and sufficient conditions are given in terms of the uniformly square integrability of the fundamental operator family and the uniform boundedness of its resolvent on the imaginary axis.

引用

页码：555 / 568

页数：14

共 18 条

[1] [Anonymous], 1999, GRADUATE TEXTS MATH
[2] Lack of time-delay robustness for stabilization of a structural acoustics model
Avalos, G
Lasiecka, I
Rebarber, R
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (05) : 1394 - 1418
[3] BATKAI A, 2000, TUBINGER BERCHTE FUN, V9, P69
[4] CORDUNEANU C, 1972, P EQ CZECH C DIFF EQ, V3, P105
[5] NOT ALL FEEDBACK STABILIZED HYPERBOLIC SYSTEMS ARE ROBUST WITH RESPECT TO SMALL TIME DELAYS IN THEIR FEEDBACKS
DATKO, R
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1988, 26 (03) : 697 - 713
[6] DATKO R, 1986, SIAM J CONTROL OPTIM, V24, P69
[7] Hale JK, 2001, OPER THEORY ADV APPL, V122, P275
[8] Huang F., 1985, ANN DIFF EQNS, V1, P45
[9] Huang F. L., 1986, CHINESE J MATH, V6, P183
[10] LI XJ, 1993, SCI CHINA SER A, V36, P1453

← 1 2 →