Open Access

Fixed points and controllability in delay systems

Fixed Point Theory and Applications20062006:41480

https://doi.org/10.1155/FPTA/2006/41480

Received: 9 December 2004

Accepted: 6 July 2005

Published: 23 February 2006

Abstract

Schaefer's fixed point theorem is used to study the controllability in an infinite delay system . A compact map or homotopy is constructed enabling us to show that if there is an a priori bound on all possible solutions of the companion control system , then there exists a solution for . The a priori bound is established by means of a Liapunov functional or applying an integral inequality. Applications to integral control systems are given to illustrate the approach.

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Authors’ Affiliations

(1)
Department of Mathematics, Northeast Normal University
(2)
Department of Mathematics and Computer Science, Fayetteville State University

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Copyright

© H. Gao and B. Zhang 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.