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

ANZIAM J. 47 (2006), 555-568

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

Faming Guo
School of Applied Mathematics and
School of Electronic Engineering
University of Electronic Science
and Technology of China
Chengdu 610054
P. R. China
guofm@uestc.edu.cn

Bin Tang
School of Electronic Engineering
University of Electronic Science
and Technology of China
Chengdu 610054
P. R. China

and

Falun Huang
Mathematical College
Sichuan University
Chengdu 610064
P. R. China

Abstract

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.

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