1990 • 656 Pages • 13.89 MB • English

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Progress in Systems and Control Theory Volume 4 Series Editor Christopher I. Byrnes, Washington University Associate Editors S.-1. Amari, University of Tokyo, Japan B.D.O. Anderson, Australian National University, Canberra, Australia Karl J. AstrOm, Lund Institute of Technology, Lund, Sweden Jean-Pierre Aubin, CEREMADE, Paris, France H.T. Banks, University of Southern California, Los Angeles, California John S. Baras, University of Maryland, College Park, Maryland A. Bensoussan, INRIA, Paris, France John Bums, Virginia Polytechnic Institute, Blacksburg, Virginia Han-Fu Chen, Beijing University, People's Republic of China M.H.A. Davis, Imperial College of Science and Technology, London, England Wendell Fleming, Brown University, Providence, Rhode Island Michel Riess, CNRS-ESE, Gif-sur-Yvette, France Keith Glover, University of Cambridge, Cambridge, England D. Hinrichsen, University of Bremen, Federal Republic of Germany Alberto Isidori, University of Rome, Italy B. Jakubczyk, Academy of Sciences, Warsaw, Poland Hidenori Kimura, Osaka University, Japan Arthur Krener, University of California, Davis H. Kunita, Kyushu University, Japan Alexandre Kurzhansky, IIASA, Laxenburg, Austria Harold M. Kushner, Brown University, Providence, Rhode Island Anders Lindquist, Royal Institute of Technology, Stockholm, Sweden Andrzej Manitius, George Mason University, Fairfax, Virginia Clyde F. Martin, Texas Tech University, Lubbock, Texas Sanjoy Mitter, Massachusetts Institute of Technology, Cambridge, Massachusetts Giorgio Picci, LADSEB-CNR, Padova, Italy Boris Pshenichnyj, Glushkov Institute of Cybernetics, Kiev H.J. Sussmann, Rutgers University, New Brunswick, New Jersey T.J. Tam, Washington University, St. Louis, Missouri V.M. Tikhomirov, Institute for Problems in Mechanics, Moscow Pravin P. Varaiya. University of California. Berkeley Jan C. Willems. University of Groningen, The Netherlands W.M. Wonham. University of Toronto

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M.A. Kaashoek I.H. van Schuppen A.C.M. Ran Editors Robust Control of Linear Systems and Nonlinear Control Proceedings of the International Symposium MTNS-89, Volume II Birkhauser 1990 Boston . Basel . Berlin

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M.A. Kaashoek I.H. van Schuppen Faculteit Wiskunde en Informatica Centre for Mathematics & Computer Science Vrije Universiteit P.O. Box 4079 De Boelelaan 1081 1009 AB Amsterdam. The Netherlands 1081 HV Amsterdam. The Netherlands A.C.M. Ran Faculteit Wiskunde en Informatica Vrije Universiteit De Boelelaan 108l 1081 HV Amsterdam. The Netherlands Library of Congress Cataloging-in-Publication Data Proceedings of the International Symposium MTNS-89 1 M.A. Kaashoek. J.H. van Schuppen. A.C.N. Ran. editors. p. cm. - (Perspectives in control theory ; v. 3-5) "The 1989 International Symposium on the Mathematical Theory of Networks and Systems (MTNS) ... held in Amsterdam. The Netherlands. June 19-23. 1989·~Pref. Contents : v. 1. Realization and modelling in system theory - v. 2. Robust control of linear systems and nonlinear control - v. 3. Signal processing. scattering and operator theory. and numerical methods. 1. System analysis-Congresses. 2. Control theory-Congresses. I. Kaashoek. M. A. II. Schuppen. J. H. van. m. Ran. A. C. M. IV. International Symposium on the Mathematical Theory of Networks and Systems (9th : 1989 : Amsterdam. Netherlands) V. Series. QA402.P766 1990 003-dc20 90-1003 CIP Printed on acid-free paper. © Birkhauser Boston, 1990 Softcover reprint of the hardcover 1st edition 1990 All rights reserved. No part of this publication may be reproduced. stored in a retrieval system. or transmitted, in any form or by any means, electronic. mechanical. photocopying. recording or other- wise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use. or the internal or personal use of specific clients. is granted by Birkhauser Boston. Inc .. for libraries and other users registered with the Copy- right Clearance Center (CCC). provided that the base fee of $0.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress Street. Salem. MA 01970. U.S.A. Special requests should be addressed directly to Birkhauser Boston, Inc .. 675 Massachusetts Avenue. Cambridge, MA 02139. U.S.A. ISBN-13:978-1-4612-8839-8 e-ISBN-13:978-1-4612-4484-4 DOl: 10.1007/978-1-4612-4484-4 Camera-ready text provided by the individual authors. 9 8 7 654 3 2 1

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Preface This volume is the second of the three volume publication containing the proceedings of the 1989 International Symposium on the Mathemat- ical Theory of Networks and Systems (MTNS-89), which was held in Amsterdam, The Netherlands, June 19-23, 1989 The International Symposia MTNS focus attention on problems from system and control theory, circuit theory and signal processing, which, in general, require application of sophisticated mathematical tools, such as from function and operator theory, linear algebra and matrix theory, differential and algebraic geometry. The interaction between advanced mathematical methods and practical engineering problems of circuits, systems and control, which is typical for MTNS, turns out to be most effective and is, as these proceedings show, a continuing source of exciting advances. The second volume contains invited papers and a large selection of other symposium presentations in the vast area of robust and nonlinear control. Modern developments in robust control and H-infinity theory, for finite as well as for infinite dimensional systems, are presented. A large part of the volume is devoted to nonlinear control. Special atten- tion is paid to problems in robotics. Also the general theory of nonlinear and infinite dimensional systems is discussed. A couple of papers deal with problems of stochastic control and filterina.

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vi Preface The titles of the two other volumes are: Realization and Modelling in System Theory (volume 1) and Signal Processing, Scattering and Operator Theory, and Numerical Methods (volume 3). The Editors are most grateful to the about 300 reviewers for their help in the refereeing process. The Editors thank Ms. G. Bijleveld and Ms. L.M. Schultze for their professional secretarial assistance, and Mr. K. van 't Hoff for his programming support. M.A. Kaashoek J.H. van Schuppen Amsterdam A.C.M. Ran February 1990

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Contents INVITED PAPERS Nonlinear H.infinity control theory: A literature survey 1 J.A. Ball, J.W. Helton Primitives for robot control 13 D.C. Deno, R.M. Murray, K.S.J. Pister, S.S. Sastry Optimal frequency design vs. an area of several complex variables 33 J.W. Helton Feedback stabilization of nonlinear systems 61 E.D. Sontag MULTIVARIABLE FEEDBACK A monotonicity result for the periodic Riccati equation 83 S. Bittanti, P. Colaneri

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viii Results on generalized Riccati equations arising in stochastic control 95 C.E. de Souza, M.D. Fragoso LQ-Problem: The discrete-time time-varying case lO3 J.e. Engwerda The output -stabilizable subspace and linear optimal control 113 A.H.W. Geerts, M.L.J. Hautus The decomposition of (A, B) invariant subsp aces and its application 121 Han Zheng-zhi, Zhang Zhong-jun, Zheng Yu-Fan The set off eedback matrices that assign the poles of a system 129 Hu Ting Shu, Shi Song-Jiao Model matchingfor linear Hamiltonian systems 135 H.J.e. Huijberts Connective stabilization of large-scale systems: A stable factorization 143 approach M. Ikeda, Hsiang-Ling Tan Riccati equations, algebras, and invariant systems 151 H. C. Myung, A.A. Sagle Maximal order reduction ofproper transfer function matrices 159 T.J. Owens The matching condition and feedback controllability of uncertain linear sys- 177 tems I.R. Petersen Convergence properties of indefinite linear quadratic problems with receding 189 horizon H. Trentelman, J.M. Soethoudt ROBUST CONTROL Generalized stability of linear singularly perturbed systems including calcula- 197 tion of maximal parameter range E.H. Abed, L. Saydy, A.L. Tits

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ix Convex combinations of Hurwitz functions and its applications to robustness 205 analysis Y.K. Foo, Y.C. Soh Designing strictly positive real transfer function families: A necessary and 215 sufficient condition for low degree and structured families c.y. Hollot, Lin Huang, Zhong-Ling Xu Quadratic stabilizability of linear systems with structural independent time 229 varying uncertainties Kehui Wei A finite zero exclusion principle 239 A. Rantzer Design of controller with asymptotic disturbance attenuation 247 K. Uchida, M. Fujita, E. Shimemura H-INFINITY CONTROL Gas turbine control using mixed sensitivity H-infinity optimisation 255 D. Biss, K. Woodgate Nonlinear H-infinity Theory 267 C. Foias, A. Tannenbaum 277 A J-spectralfactorization approach to H-infinity control M. Green, J. Doyle, K. Glover, D.J.N. Limebeer 285 Vector interpolation, H-infinity control and model reduction M. Green, D.J.N. Limebeer 293 Sensitivity minimization and robust stabilization by stable controller S. Hara, M. Yidyasagar Conjugation and H-infinity control 301 H. Kimura Necessary and sufficient conditions for the existence of H-infinity controll- 309 ers: An interpolation approach D.J.N. Limebeer, E.M. Kasenally

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x ·On H-infinity contro' LQG control and minimum entropy 317 D. Mustafa Optimal H-infinity SISO-controllers with structural constraints 329 S. Pohjolainen Super optimal H -infinity design 339 I. Postlethwaite, D.W. Gu, M.C. Tsai H -infinity control with state feedback 347 AA. Stoorvogel ADAPTIVE CONTROL Convergence analySiS of self-tuning controllers by Bayesian embedding 355 P.R. Kumar On bounded adaptive control with reduced prior knowledge 361 R. Ortega, L. Praly, Yu Tang Indirect techniques for adaptive input output linearization of nonlinear sys- 369 tems A. Teel, R. Kadiyala, P.V. Kokotovic, S.S. Sastry STOCHASTIC CONTROL AND FILTERING Interpolation approach to the H-infinity filter problem 387 D. Ho, A. Elsayed, M.J. Grimble, U. Shaked Stochastic disturbance decoupling 397 H. Inaba, N. Otsuka Discrete-time filtering for linear systems in correlated noise with non- 407 Gaussian initial conditions: Formulas and asymptotics R.B. Sowers, A.M. Makowski NONLINEAR CONTROL Boundary feedback stabilization of distributed parameter systems 421 C.I. Byrnes, D.S. Gilliam Optimal nonlinear feedback system design for a general tracking problem 429 Guanrong Chen, R.J.P. de Figueiredo

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