Stabilization of Linear Systems with Both State and Input Delays
This chapter studies the stabilization problem of some classes of linear systems with both state and input time-varying delays. Three classes of time-delay systems are considered. The first class of systems consists of a chain of delayed integrators which
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Truncated Predictor Feedback for Time-Delay Systems
Truncated Predictor Feedback for Time-Delay Systems
Bin Zhou
Truncated Predictor Feedback for Time-Delay Systems
123
Bin Zhou Harbin Institute of Technology Harbin, China
ISBN 978-3-642-54205-3 ISBN 978-3-642-54206-0 (eBook) DOI 10.1007/978-3-642-54206-0 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014936990 © Springer-Verlag Berlin Heidelberg 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Zhaoyan and Chengyin
Preface
Time-delay systems have received much attention during the past several decades because they have very wide applications in engineering practice such as chemical process control, machining, combustion systems, teleoperation, and networked systems. Time-delay systems as special cases of distributed parameter systems are infinite-dimensional and thus are hard to be dealt with in both mathematics and in practice. For linear systems with state and/or input delays that are relatively small compared with the plant’s time scales, finite-dimensional feedback laws designed by standard algorithms such as pole assignment and linear quadratic regulator are still applicable since every linear system possesses a robustness margin to small delays. This is
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