Piecewise Linear Modeling and Analysis
Piecewise Linear (PL) approximation of non-linear behaviour is a well-known technique in synthesis and analysis of electrical networks. However, the PL description should be efficient in data storage and the description should allow simple retrieval of th
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PIECEWISE LINEAR MODELING AND ANALYSIS
by
DOMINE M. W. LEENAERTS and
WIM M. G. VAN BOKHOVEN Eindhoven University a/Technology
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
ISBN 978-1-4419-5046-8 ISBN 978-1-4757-6190-0 (eBook) DOI 10.1007/978-1-4757-6190-0
Printed on acid-free paper
All Rights Reserved © 1998 Springer Science+Business Media New York Originally published by K1uwer Academic Publishers in 1998 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
To Lisanne for here love and support D.MW. Leenaerts
CONTENTS
Preface ...........................................................................................·... 11 1. The state model of a piecewise linear network ................. 15
1.1.
Model descriptions .................................................................. 15
1.2.
The ideal diode ........................................................................ 16
1.3.
Electrical networks and PL models ........................................ 18
1.4.
The states in a Phmapping .................................................... 21
1.5.
The partitioning of the state space ......................................... 23
1.6.
Properties of a PL mapping ....................... ~..-' ....~'-..................... 25
1.7.
The complete PL model description ........ ~ .............................. 26
1.8.
Conclusions ............................................................................. 29
2. Piecewise linear model descriptions .................................. 31
2.1.
Fundamentals and definitions ................................................ 31
2.2.
Explicit PL model descriptions ............................................... 34
2.2.1.
The model description of Chua .............................................. 35
2.2.2.
The model description of Giizelis ........................................... 37
2.2.3.
The model description of Kahlert .......................................... 39
2.2.4.
The model description of Huertas .......................................... 42
2.3.
Implicit PL model descriptions ............................................... 43
2.3.1.
The model description of van Bokhoven, model 1 ............... 43
2.3.2.
The model description of van Bokhoven, model 2 ............... 46
2.4.
Comparison of the models ...................................................... 47
2.4.1.
Model Chua ..................•........................................................... 47
2.4.2.
Model Giiz ................................................................................ 49
2.4.3.
Model Kah •.....................•...........•...•...•...........•.•.•••.•..•.•.•••.....••• 50
8
2.4.4.
Model Bok2 ......•........•......•............•..................................
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