Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays
In this brief the authors establish a new frequency-sweeping framework to solve the complete stability problem for time-delay systems with commensurate delays. The text describes an analytic curve perspective which allows a deeper understanding of spectra
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Xu-Guang Li Silviu-Iulian Niculescu Arben Çela
Analytic Curve FrequencySweeping Stability Tests for Systems with Commensurate Delays
SpringerBriefs in Electrical and Computer Engineering Control, Automation and Robotics
Series editors Tamer Başar Antonio Bicchi Miroslav Krstic
More information about this series at http://www.springer.com/series/10198
Xu-Guang Li Silviu-Iulian Niculescu Arben Çela •
Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays
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Xu-Guang Li School of Information Science and Engineering Northeastern University Shenyang, Liaoning China
Arben Çela Department of Computer Science and Telecommunication UPE, ESIEE Paris Noisy-le-Grand France
Silviu-Iulian Niculescu Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506) CNRS-CentraleSupélec-Université Paris-Sud Gif-Sur-Yvette France
ISSN 2191-8112 ISSN 2191-8120 (electronic) SpringerBriefs in Electrical and Computer Engineering ISSN 2192-6786 ISSN 2192-6794 (electronic) Control, Automation and Robotics ISBN 978-3-319-15716-0 ISBN 978-3-319-15717-7 (eBook) DOI 10.1007/978-3-319-15717-7 Library of Congress Control Number: 2015933150 Mathematical Subject Classifications: 34K06, 93B60, 93C23, 93D20 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. MATLAB® is a registered trademark of The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098, USA. http://www.mathworks.com. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
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Preface
Time-delay systems have been intensively studied in various disciplines. On one hand, delay phenomena exist in many dynamical systems encountered in engineering, physics, chemistry, biology, and economics. For instance, examples can be found in population dynamics [63], biological systems [76], as well as engineering systems [92]. On the other hand, sometime
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