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

Published online by Cambridge University Press:  17 February 2009

Faming Guo ,
Bin Tang  and
Falun Huang
Faming Guo
Affiliation:
School of Applied Mathematics and School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China; e-mail: [email protected].
Bin Tang
Affiliation:
School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China.
Falun Huang
Affiliation:
Mathematical College, Sichuan University, Chengdu 610064, P. R. China.
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Abstract

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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.

Keywords

small delayrobust stabilityfundamental operator.
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 4 , April 2006 , pp. 555 - 568
Copyright
Copyright © Australian Mathematical Society 2006

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