Mathematical Theory of Networks and Systems: Proceedings of the MTNS-83 International Symposium Beer Sheva, Israel, June 20–24, 1983

915 Pages·1984·15.72 MB·English

by  A. C. Antoulas (auth.), P. A. Fuhrmann (eds.)

Lecture Notes in
Control and
Information Sciences
Edited by A.V. Balakrishnan and M.Thoma
58
Mathematical Theory of
Networks and Systems
Proceedings of the MTNS-83 International Symposium
Beer Sheva, Israel, June 20-24, 1983
Edited by RA. Fuhrmann
Springer-Verlag
Berlin Heidelberg New York Tokyo 1984
Series Editors
A.V. Balakrishnan • M. Thoma
Advisory Board
L. D. Davisson • A. G. J. MacFarlane • H. Kwakernaak
J. L. Massey • Ya. Z. Tsypkin • A. J. Viterbi
Editor
Paul A. Fuhrmann
Dept. of Mathematics and Computer Science
Ben-Gurion University of the Negev
Beer Sheva 84120
Israel
AMS Subject Classifications (1980): 9306, 9406
ISBN 3-540-13168-X Springer-Verlag Berlin Heidelberg New York Tokyo
ISBN 0-387-13168-X Springer-Verlag New York Heidelberg Berlin Tokyo
This work is subject to copyright. All rights are reserved, whether the whole or p~.rt of the material
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payable to "Verwertungsgeseltschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1984
Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/13ergstr.
2061/3020-543210
This volume is dedicated to M.S. Livsic -
a man of great courage, intellect and vision.
SYMPOS I~UM CHAIRMAN:
P.A. Fuhrmann
~NS ORGANIZING COMMITTEE:
P.A. Fuhrmann, J.S. Baras, R.W. Brockett, P. Dewilde, H. Dym,
A. Peintuch, I.C. Go,berg, D. Hinrichsen, R. Saeks
~NS PROGRAM COMMITrEE:
C. Byrnes, M.L.J. Hautus, M. Hazewinkel, J.W. Helton, H. Heymann,
A. Isidori~ T. Kailath, R.E. Kalman, E.W. Kamen, P. Krishnaprasad,
M.S. Livsic, G. Marchesini, S.K. Mitter, A.S. Morse, H.Fo Munzner,
W. Porter, L.M. Silve~man, E.D. Sontag, H.J. Sussmann, D. Tabak,
A. Tannenbaum, J.C. Willems, H.S. Witsenhausen
MTNS STEERING CO~ITrEE:
W.N. Anderson, R. deSantis, C.A. Desoer, P. Dewilde [Chairman],
A. Peintuch, I.C. Gohberg, J.W. Helton, N. Levan, R.W. Newcomb,
W.A. PorteT, R. Sacks, G.E. TTapp, A. Zemanian.
PREFACE
This volume is based on the lectures presented at the
International Symposium of Networks and Systems (MTNS-83)
held at the campus of Ben Gurion University of the Negev,
June 20-24, 1983.
The symposium was supported by Ben Gurion University of
the Negev and The Israeli Academy of Sciences, as well as
indirectly by the United States NSF which provided a signifi-
cant block travel grant for American participants. All this
support is greatly appreciated.
Several persons took active part in the organization of
the conference and the setting up of the special sessions.
Especially I would like to mention A. Bultheel, C.I. Byrnes,
P. Dewilde, I.C. Gohberg, D. Hinrichsen, E. Jonckheere,
A. Lindquist, E.D. Sontag and R. Saeks. Y. Magen the
Academic Secretary of Ben Gurion University was particularly
helpful. To all of them I am deeply grateful.
It is with growing satisfaction that we note that the
MINS conference has become a regular meeting ground for Net-
work and System Theorists and Mathematicians. That the
attendance and high standards are keeping up attests to the
continuing need for such a meeting and to its importance to
all participants.
Pau l A. Fuhrmann
Beer Sheva
October 1983
TABLE OF CONTENTS
A.C. ANTOULAS On the Design Problem for Linear Systems
J.A. BALL, Linear Fractional Par~meterizations of Matrix
J.W. HELTON Function Spaces and a New Proof of the Youla-
Jabr-Bongiorno Parametrization for Stabilizing 16
Compensators
Y. BARAM Minimal Order Representation, Estimation and
Feedback of Continuous-Time Stochastic Linear
Systems 24
H. BART, I. GOHBERG, Wiener-Hopf Factorization and Realization 42
M.A. KAASHOEK
Z. BARTOSIEWICZ Closedness of an Attainable Se t of a Delay
System 63
Y. BISTRITZ A New Unit Circle Stability Criterion 69
O.H. BOSGRA On t h e Structure and Pa r a m e t r i z a t i o n of Non-
Minimal Partial Realizations 88
S. BOYD, L.O. CHUA, Uniqueness of Circuits and Systems Containing
One Nonlinearity 101
R.W. BROCKETT Robotic Manipulators and the Product of
Exponential Formula 120
A. BULTHEEL Applications of Pade Approximants and
Continued Fractions 130
C.I. BYRNES Toward a Global Theory of (f,g)-Invariant
Distribution with Singularities 149
g. CONTE, A.M. PERDON An Algebraic Notion of Zeros for Systems
Over Rings 166
R.F. CURTAIN On Semigroup Formulations of Unbounded Obse rv -
a t i o n s and Control Action for Distributed
Systems 183
P. DELSARTE, Y. GENIN Spectral Properties of Finite Toeplitz
Matrices 194
U.B. DESAI S t o c h a s t i c Model Reduc t ion and Reduced-
Orde r Kalman-Bucy F i l t e r i n g 214
IX
P. DEWILDE Spectral Approximation and Estimation with
Scattering Functions 234
P. DEWILDE Or tho g o n a l F i l t e r s : A Numer ica l Approach to
F i l t e r i n g Theory 253
V. DOLEZAL Generalized Solutions of Semistate Equations 268
A, DRAUX Formal Orthogonal Polynomials and Fade
Approximants in a Non-Commutative Algebra 278
H. DYM Un i t a r y I n t e r p o l a t i o n , F a c t o r i z a t i o n I n d i c e s
and Block Hankel M a t r i c e s 293
B, DZIURLA, A Continuation-Type Method for Solving
R.W. NEWCOMB Equations 299
R, EISINC The Distance Between a System and the Set of
Uncontrollable Systems 303
A. FEINTUCH The Resolution Topology and Internal
St~ilization 315
M. FLIESS On the Inversion of Nonlinear Multivariable
Systems 323
E. FORNASINI, On Some Connections Between 2D Systems Theory
G. MARCHESINI and the Theory of Systems Over Rings 331
B.A. FRANCIS, H ~ - Optimal Feedback Controllers for Linear
J,W. HFLTON, g. ZAMES Multivariable Systems 347
I. GOHBERG, A Sign Characteristic for Selfadjoint
P. LANCASTER, Rational Matrix Functions 363
L. RODMAN
D. GOL LMANN Partial Realization by Discrete-Time Inter-
nally Bilinear Systems: An Algorithm 370
R. GROSSMAN, Approximation and Control of Symmetric
C. MARTIN Systems on the Circle 376
S.J. }I~RLING A Canonical Form for the Algebraic Riccati
M.A. SINGER Equation 389
P. HARSHAVARDIIANA, Stochastic Balancing and Approximation-
406
E.A. JONCKHEERE, Stability and Minimality
L.M. SI LVERMAN
M.L,J. HAUTUS Disturbance Rejection for Systems over Rings 427
M. HAZEWINKEL The Linear Systems Lie Algebra, the Segal-
Shale-Weil Representation and all Kalman-
Bucy Filters 433
M. HAZEWINKEL, Specia l S t ruc tu re , D e c e n t r a l i z a t i o n and
C.F. MARTIN Symmetry fo r Linear Systems 437
D. HINRICHSEN, A Canonical Form for Static Linear Output
D.PRATZEL-WOLTERS Feedback 441
L.R. HUNT, G, MEYER, Nonlinear Control of Aircraft 463
R. SU
A. ISIDORI Nonlinear Feedback, Structure at Infinity and
the Input-Output Linearization Problem 473
E.A. JONCKHEERE Principal Component Analysis of Flexible
Systems - Open-Loop Case 494
E. JONCKHEERE, Reduced Compensator Design via Log-Balancing -
Ph. OPDENACKER, a Case Study 513
L. SILVERMAN
E.W. KAMEN, A LocalTheory of Linear Systems with Non-
P.P. KHARGONEKAR, Commensurate Time Delays 521
A. TANNENBAUM
D. KANEVSKY An Approach to the Description of Some
Algebraic Varieties Arising in System Theory 541
A. KASINSKI, A Fast Graph Theoretic Algorithm for the
J. LEVINE Feedback Decoupling Problem of Nonlinear
Systems 550
P.P. KHARGONEKAR On the Regulator Problem with Internal
563
A.B. OZGULER Stability
g.J. LNOWLES, Sta te Space Theory - A Banach Space Approach 574
R. SAEKS
N. KRAVITSKY On Determinantal Representa t ion o f Algebraic
Curves 584
P.S. KRISHNAPRASAD On Certain Infinite-Dimensional Lie Algebras
and Related System-Theoretic Problems 591
R.P. KURSHAN Coordination of Concurrent Probabilistic
Processes 605
F. LA/~qABHI-LAGARRIGUE A Volterra Series Interpretation of Some
Higher Order Conditions in Optimal Control 615
E.B, LEE, S.H. ZAK Remarks on Minimal Realizations of 2-D
Systems 628
A. LEPSCHY, U. VIARO Some Problems in Model Order Reduction
639
Using Frequency-Domain Methods
Xl
S. LEVIN Distributed Systems and their Transfer
Function 657
M.S. LIVSIC System Theory and Wave Dispersion 663
J.-CI, LOUIS, On Exact Controllability in Hilbert Spaces 676
D. WEXLER
A. LINDQUIST, Forward and Backward Semimartingale Represen-
G. PICCI tations for Stationary Increments Processes 686
R. MARINO, G. CESAREO Nonlinear Control Theory and Symbolic
Algebraic Manipulations 725
A.S. MORSE A Sunmlary of Recent Results on Deadbeat 741
Control Using Periodic Feedback
M. PONTIER, Stochastic Control with Average Constraint 753
J. SZPIRGLAS
A.G. RAMM Analytic Theory of Random Fields Estimation
and Filtering 764
J.A. RENE KE A Strategy for Decentralized Control of
Stably Connected Systems 774
F.M. REZA The Concept of Power Dominant Systems 787
K. SEtTZ A Lattice Theoretical Characterization of
Network Systems 796
M.A. SHAYMAN A Complete Phase Portrait for the Matrix
Riccati Equation 804
E.D. SONTAG An Approximation Theorem in Nonlinear
Sampling 806
H.J. SUSSMANN Some Recent Results on Pathwise Nonlinear
Filtering 813
H.J. SUSSMANN A Lie-Volterra Expansion for Nonlinear
822
Systems
A.R. TANNENBAUM, On Weak Po le P lacement o f L inea r Systems
P .P . KHARGONEKAR Depending on Pa ramete r s 829
T.J. TARN, J.W. CLARK, Analytic Controllability of Quantum-Mechanical
G.M. HUANG Systems 840
E.A. TRACHTENBERG Systems ovew Finite Groups as Suboptimal
Wiener Filters: A Comparative Study 856
Xll
P. VAN DOOREN A Unitary Method for Deadbeat Control 864
J.H. van SCHUPPEN Dissipative Stochastic Control Systems 881
V. VINNIKOV Determinantal Representa t ions of Real Cubics
and Canonical Forms of Corresponding Triples
of Matrices 882
J.C. WILLEMS Modelling a Time Series by a Linear Time-
Invariant System 899
E. ZEHEB Output Feedback Stabilization of Delay Linear
Systems with Uncertain Parameters 903