Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects
This book is all about finite wordlength errors in digital filters, con trollers and estimators, and how to minimize the deleterious effects of these errors on the performance of these devices. This does by no means imply that all about finite wordlength
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Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects
With 60 Figures
Springer-Verlag London Berlin Heidelberg New York Paris Tokyo Hong Kong Barcelona Budapest
Michel Gevers, PhD Centre for Systems Engineering and Applied Mechanics (CESAME), Universite Catholique de Louvain, Bitiment Euler, B-1348 Louvain-Ia-Neuve, Belgium Gang Li, PhD School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 2263
ISBN-13:978-1-4471-2041-4 DOl: 10.1007/978-1-4471-2039-1
e-ISBN-13:978-1-4471-2039-1
British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers.
c Springer-Verlag London Limited 1993 Softcover reprint of the hardcover 1st edition 1993 The publisher makes no representation, express or implied, with regard' to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera ready by authors 69/3830-543210 Printed on acid-free paper
Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects
Communications and Control Engineering Series Editors: B.W. Dickinson·A. Fettweis·J.L. Massey·J.W. Modestino E.D. Sontag· M. Thoma
CCES published titles include: Sampled-Data Control Systems J. Ackermann Interactive System Identtfication T. Bohlin The Riccatti Equation S. Bittanti, AJ. Laub and J.C. Willems (Eds.)
Nonlinear Control Systems A.Isidori Analysis and Design of Stream Ciphers R.A. Rueppel Sliding Modes in Control Optimization V.1. Utkin
Fundamentals of Robotics M. Vukobratovi6
To my parents
- Michel Gevers
To Qian-Rong
- Gang Li
Contents Preface
xi
1 Introduction 1.1 Motivation and general statement of objectives 1.2 A historical view and some motivating examples 1.3 Outline of the book. . . . . . . . . . . . . . . .
1 1 4 17
2 Finite Word Length errors and computations 2.1 Introduction . . . . . . . . . . . ~ . 2.2 Representations of binary numbers . . . . . . 2.3 Overflow and quantization errors . . . . . . . 2.4 Arithmetic computations and roundoff errors 2.5 Dynamic range and scaling 2.6 Conclusions . . . . . . . . . . . . . . . . . .
23 23 25 29 33 39 43
3 Parametrizations in digital system design 3.1 Introduction.................. 3.2 State space realization set . . . . . . . . . . 3.3 Sen
