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Fixed points and controllability in delay systems

Fixed Point Theory and Applications volume 2006, Article number: 41480 (2006) Cite this article

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 and Affiliations

  1. Department of Mathematics, Northeast Normal University, Changchun, Jilin, 130024, China

    Hang Gao

  2. Department of Mathematics and Computer Science, Fayetteville State University, NC, Fayetteville, 28301-4298, USA

    Bo Zhang

Authors
  1. Hang Gao
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  2. Bo Zhang
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Correspondence to Bo Zhang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Gao, H., Zhang, B. Fixed points and controllability in delay systems. Fixed Point Theory Appl 2006, 41480 (2006). https://doi.org/10.1155/FPTA/2006/41480

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

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