The Riccati Equation
Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known a
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Sergio Bittanti . Alan 1. Laub
lan C.Wi11ems (Eds.)
THE
RICCATI EQUATION
Springer-Verlag Berlin Heidelberg GmbH
Editors: Sergio Bittanti Politecnico di Milano, Dipartimento di Elettronica, Piazza Leonardo da Vinei 32,1-20133 Milano, ltaly AlanJ.Laub Department ofElectrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA lan C.Willems Department of Mathematics, University of Groningen, P. O. Box 800, NL-9700 AV Groningen, The Netherlands
Frontispiece: Portrait ofCount Jacopo Riccati reproduced by courtesy of the municipallibrary of Castelfranco Veneto (TV), ltaly
ISBN 978-3-642-63508-3 Library of Congress Cataloging-in-Publication Data The Riccati equation / S. Bittanti, A. J. Laub, 1. C. Willems, editors. (Communications and control engineering series) Includes index. ISBN 978-3-642-63508-3 ISBN 978-3-642-58223-3 (eBook) DOI 10.1007/978-3-642-58223-3 J. Riccati equation.1. Bittanti, Sergio. II. Laub, Alan J. III. Willems, Jan C. IV. Series. 1948- . QA37J.R36 1991 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed, specifically the rights of translation, reprinting, re-use of iIIustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provision of the German Copyright Law of September 9, 1965, in its current version and a copyright fee must always be paid. Violations fali underthe prosecution act ofthe German Copyright Law. © Springer-Verlag Berlin Heidelberg 1991 Originally published by Springer-Verlag Berlin Heidelberg New York in 1991 Softcover reprint ofthe hardcover Ist edition 1991 The use of registered names, trademarks, etc. in this publiclation 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. Typesetting: Text supplied by authors, formatted by Danny L. Lewis, Buchproduktion Berlin, with T EX; 6113020-543210
Preface
Conceived byCountJacopo Francesco Riccati more thana quarter ofa millennium ago, the Riccati equation has been studied in subsequent centuries by a number of distinguished scientists, including several members of the Bernoulli family, L. Euler and 1. Liouville, to name but a few. The last thirty years have witnessed a considerable renaissance ofthe research around this equation, stemming from the widespread developments in and diffusion of systems and control concepts and applications. Indeed, since its introduction in control theory at the beginning of the sixties, the Riccati equation has known an impressive range ofapplications, such as linear quadratic optimal control, stability theory, stochastic filtering and stochastic control, synthesis oflinearpassive networks, differential games and, more recently, Hoo-control and robust stabilization. The state ofthe art in this area was reviewed at a recent Workshop on the Riccati Equation in Con
