Stability of Time-Delay Systems
This monograph is a self-contained, coherent presentation of the background and progress of the stability of time-delay systems. Focusing on techniques, tools, and advances in numerical methods and optimization algorithms, the authors developed material w
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Editorial Advisory Board Okko Bosgra Delft University The Netherlands
William Powers Ford Motor Company (retired) USA
Graham Goodwin University of Newcastle Australia
Mark Spong University of Illinois Urbana-Champaign USA
Petar Kokotovic University of California Santa Barbara USA Manfred Morari ETH ZUrich, Switzerland
lori Hashimoto Kyoto University Kyoto, Japan
Keqin Gu Vladimir L. Kharitonov Jie ehen
Stability of Time-Delay Systems
Springer Science+Business Media, LLC
KeqinGu Southem illinois University at Edwardsville Department of Mechanical and Industrial Engineering Edwardsville, IL 62026-1805 USA
Vladimir L. Kharitonov CINVESTAV-IPN Department of Automatic Control A.P. 14-740, Mexico, D.F. Mexico
Jie Chen University of California at Riverside Department of Electrical Engineering Riverside, CA 92521 USA
Library of Congress Cataloging-in-Publication Data Gu, Keqin, 1957Stability of time-delay systems / Keqin Gu, Jie Chen, Vladimir L. Kharitonov. p. cm.- (Control engineering) Includes bibliographical references and index. ISBN 978-1-4612-6584-9 ISBN 978-1-4612-0039-0 (eBook) DOI 10.1007/978-1-4612-0039-0 1. Automatic control. 2. Time-delay systems. 3. Stability. 1. Chen, Jie, 1963- II. Kharitonov, Vladimir, L. 1950- III. TitIe. TJ213.G83 2003 629.~c21
2003041932 CIP Printed on acid-free paper. @2003Springer Science+Business Media New York OriginaIly published by Birkhăuser Boston in 2003 Softcover reprint of the hardcover 1st edition 2003 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis.Use in connection with any form ofinformation storage and retrieval, electronic adaptation, computersoftware, or by similar or dissimilar methodology now known or hereafter developed is forbidden . The use of general descriptive names, trade names, trademarks , etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
ISBN 978-1-4612-6584-9
Typeset by the authors.
987 6 5 4 3 2 1
SPIN 10782604
KG dedicates the book to his parents Lijan Gu and Jieping Jiang for their love and support. VK dedicates the book to his teacher, the late Professor Vladimir Ivanovich Zubov (1930-2000) for his friendship and mentorship. JC dedicates the book to his wife Yan and sons Christopher and Stephen for their love and trust.
Contents Preface
xiii
Notation
xix
1 Introduction to Time-Delay Systems 1.1 Introduction . . . . . . . . . . . . 1.2 A simple time-delay system . . . 1.3 Functional differential equations
1
1.4 Stability of time-delay systems 1.4.1 Stability concept . . . . .
10
1.4.2
Lyapunov-Krasovskii Theorem
1.4.3 Razumikhin Theorem 1.5 Linear systems . . . . . . . . 1.6 Linear time-invariant systems 1. 7 Neutral time-delay systems 1.8 Outline of the
