Qualitative Theory of Hybrid Dynamical Systems
Hybrid dynamical systems, both continuous and discrete dynamics and variables, have attracted considerable interest recently. This emerging area is found at the interface of control theory and computer engineering, focusing on the analogue and digital asp
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Editorial Advisory Board Okko Bosgra Delft University The Netherlands
William Powers Ford Motor Company USA
Graham Goodwin University of Newcastle Australia
Mark Spong University of Illinois Urbana-Champaign USA
Petar Kokotovi6 University of California Santa Barbara USA Manfred Morari ETH Zurich, Switzerland
fori Hashimoto Kyoto University Kyoto, Japan
Qualitative Theory of Hybrid Dynamical Systems Alexey s. Matveev Andrey v. Savkin
With 88 Figures
Springer Science+Business Media, LLC
Alexey S. Matveev Department of Mathematics and Mechanics St. Petersburg University St. Petersburg, Russia
Andrey V. Savkin Department of Electrical and Electronic Engineering University of Western Australia Perth 6907, Australia
Library of Congress Cataloging-in-Publication Data Matveev, Alexey S. Qualitative theory of hybrid dynamical systems / Alexey S. Matveev, Andrey Savkin. p. cm.-(Control engineering) Inc1udes bibliographical references and index. ISBN 978-1-4612-7114-7 ISBN 978-1-4612-1364-2 (eBook) DOI 10.1007/978-1-4612-1364-2 1. Electronic controllers. 2. Digital control systems. 3. Analog electronic systems. 1. Savkin, Andrey V. II. Title. III. Control engineering (Birkhli.user) TK7881.2.M38 2000 629.8'9-dc21 99-052603 CIP AMS Subject Classifications: 93B, 93C Printed on acid-free paper. © 2000 Springer Science+Business Media New York Originally published by Birkhli.user Boston in 2000 Softcover reprint of the hardcover 1sI edition 2000 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission ofthe publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, 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 byanyone. ISBN 978-1-4612-7114-7 Typeset by the authors using TeX.
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Contents
Preface 1 Introduction 1.1 Hybrid Dynamical Systems . . . . . . . . . . . . . . 1.2 Two Contrasting Examples of Discretely Controlled Continuous Variable Systems 1.3 The Main Goal of This Book 1.4 Organization of the Book 1.5 List of Notations . . . . . . . 2
Qualitative Analysis of Some Simple Hybrid Dynamical Systems 2.1 Introduction....... . .. .. . . . . . . . 2.2 Differential Automata and Their Trajectories 2.3 Cyclic Linear Differential Automata 2.4 Qualitative Analysis of Cyclic Linear Differential Automata . . . . . . . . 2.5 Switched Server Systems with a Cyclic Switching Policy 2.6 Switched Server Systems with Several Limit Cycles . . . 2.7 Qualitative Analysis of Closed Switched Server Systems 2.8 Essentially Non-Periodic Dynamics of Switched Arrival Systems . . .
