Vincent D. Blondel / Alexandre Megretski (eds.)

Unsolved Problems in Mathematical Systems and Control Theory

Herausgeber: Blondel, Vincent D.; Megretski, Alexandre

• Gebundenes Buch

Produktbeschreibung

This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.

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Produktdetails

• Verlag: Princeton University Press
• Seitenzahl: 354
• Erscheinungstermin: 26. Juli 2004
• Englisch
• Abmessung: 240mm x 161mm x 24mm
• Gewicht: 713g
• ISBN-13: 9780691117485
• ISBN-10: 0691117489
• Artikelnr.: 21498331

Autorenporträt

Edited by Vincent D. Blondel & Alexandre Megretski

Inhaltsangabe

Frontmatter Preface xiii Associate Editors xv Website xvii
PART 1. LINEAR SYSTEMS 1 Problem 1.1. Stability and composition of transfer
functions Guillermo Fernández-Anaya, Juan Carlos Martínez-García 3 Problem
1.2. The realization problem for Herglotz-Nevanlinna functions Seppo Hassi,
Henk de Snoo, Eduard Tsekanovskii 8 Problem 1.3. Does any analytic
contractive operator function on the polydisk have a dissipative scattering
nD realization? Dmitry S. Kalyuzhniy-Verbovetzky 14 Problem 1.4. Partial
disturbance decoupling with stability Juan Carlos Martínez-García, Michel
Malabre, Vladimir Kucera 18 Problem 1.5. Is Monopoli's model reference
adaptive controller correct? A. S. Morse 22 Problem 1.6. Model reduction of
delay systems Jonathan R. Partington 29 Problem 1.7. Schur extremal
problems Lev Sakhnovich 33 Problem 1.8. The elusive iff test for
time-controllability of behaviors Amol J. Sasane 36 Problem 1.9. A Farkas
lemma for behavioral inequalities A.A. (Tonny) ten Dam, J.W. (Hans)
Nieuwenhuis 40 Problem 1.10. Regular feedback implementability of linear
differential behaviors H. L. Trentelman 44 Problem 1.11. Riccati stability
Erik I. Verriest 49 Problem 1.12. State and first order representations Jan
C. Willems 54 Problem 1.13. Projection of state space realizations Antoine
Vandendorpe, Paul Van Dooren 58
PART 2. STOCHASTIC SYSTEMS 65 Problem 2.1. On error of estimation and
minimum of cost for wide band noise driven systems Agamirza E. Bashirov 67
Problem 2.2. On the stability of random matrices Giuseppe C. Calafiore,
Fabrizio Dabbene 71 Problem 2.3. Aspects of Fisher geometry for stochastic
linear systems Bernard Hanzon, Ralf Peeters 76 Problem 2.4. On the
convergence of normal forms for analytic control systems Wei Kang, Arthur
J. Krener 82
PART 3. NONLINEAR SYSTEMS 87 Problem 3.1. Minimum time control of the
Kepler equation Jean-Baptiste Caillau, Joseph Gergaud, Joseph Noailles 89
Problem 3.2. Linearization of linearly controllable systems R. Devanathan
93 Problem 3.3. Bases for Lie algebras and a continuous CBH formula
Matthias Kawski 97 Problem 3.4. An extended gradient conjecture Luis Carlos
Martins Jr., Geraldo Nunes Silva 103 Problem 3.5. Optimal transaction costs
from a Stackelberg perspective Geert Jan Olsder 107 Problem 3.6. Does cheap
control solve a singular nonlinear quadratic problem? Yuri V. Orlov 111
Problem 3.7. Delta-Sigma modulator synthesis Anders Rantzer 114 Problem
3.8. Determining of various asymptotics of solutions of nonlinear
time-optimal problems via right ideals in the moment algebra G. M. Sklyar,
S. Yu. Ignatovich 117 Problem 3.9. Dynamics of principal and minor
component flows U. Helmke, S. Yoshizawa, R. Evans, J.H. Manton, and I.M.Y.
Mareels 122
PART 4. DISCRETE EVENT, HYBRID SYSTEMS 129 Problem 4.1. L2-induced gains of
switched linear systems João P. Hespanha 131 Problem 4.2. The state
partitioning problem of quantized systems Jan Lunze 134 Problem 4.3.
Feedback control in flowshops S.P. Sethi and Q. Zhang 140 Problem 4.4.
Decentralized control with communication between controllers Jan H. van
Schuppen 144
PART 5. DISTRIBUTED PARAMETER SYSTEMS 151 Problem 5.1. Infinite dimensional
backstepping for nonlinear parabolic PDEs Andras Balogh, Miroslav Krstic
153 Problem 5.2. The dynamical Lame system with boundary control: on the
structure of reachable sets M.I. Belishev 160 Problem 5.3.
Null-controllability of the heat equation in unbounded domains Sorin Micu,
Enrique Zuazua 163 Problem 5.4. Is the conservative wave equation regular?
George Weiss 169 Problem 5.5. Exact controllability of the semilinear wave
equation Xu Zhang, Enrique Zuazua 173 Problem 5.6. Some control problems in
electromagnetics and fluid dynamics Lorella Fatone, Maria Cristina
Recchioni, Francesco Zirilli 179
PART 6. STABILITY, STABILIZATION 187 Problem 6.1. Copositive Lyapunov
functions M. K. Çamlibel, J. M. Schumacher 189 Problem 6.2. The strong
stabilization problem for linear time-varying systems Avraham Feintuch 194
Problem 6.3. Robustness of transient behavior Diederich Hinrichsen, Elmar
Plischke, Fabian Wirth 197 Problem 6.4. Lie algebras and stability of
switched nonlinear systems Daniel Liberzon 203 Problem 6.5. Robust
stability test for interval fractional order linear systems Ivo Petrs,
YangQuan Chen, Blas M. Vinagre 208 Problem 6.6. Delay-independent and
delay-dependent Aizerman problem Vladimir Rasvan 212 Problem 6.7. Open
problems in control of linear discrete multidimensional systems Li Xu,
Zhiping Lin, Jiang-Qian Ying, Osami Saito, Yoshihisa Anazawa 221 Problem
6.8. An open problem in adaptative nonlinear control theory Leonid S.
Zhiteckij 229 Problem 6.9. Generalized Lyapunov theory and its
omega-transformable regions Sheng-Guo Wang 233 Problem 6.10. Smooth
Lyapunov characterization of measurement to error stability Brian P.
Ingalls, Eduardo D. Sontag 239
PART 7. CONTROLLABILITY, OBSERVABILITY 245 Problem 7.1. Time for local
controllability of a 1-D tank containing a fluid modeled by the shallow
water equations Jean-Michel Coron 247 Problem 7.2. A Hautus test for
infinite-dimensional systems Birgit Jacob, Hans Zwart 251 Problem 7.3.
Three problems in the field of observability Philippe Jouan 256 Problem
7.4. Control of the KdV equation Lionel Rosier 260
PART 8. ROBUSTNESS, ROBUST CONTROL 265 Problem 8.1. H[infinity]<-norm
approximation A.C. Antoulas, A. Astolfi 267 Problem 8.2. Noniterative
computation of optimal value in H[infinity]< control Ben M. Chen 271
Problem 8.3. Determining the least upper bound on the achievable delay
margin Daniel E. Davison, Daniel E. Miller 276 Problem 8.4. Stable
controller coefficient perturbation in floating point implementation Jun
Wu, Sheng Chen 280
PART 9. IDENTIFICATION, SIGNAL PROCESSING 285 Problem 9.1. A conjecture on
Lyapunov equations and principal angles in sub-space identification Katrien
De Cock, Bart De Moor 287 Problem 9.2. Stability of a nonlinear adaptive
system for filtering and parameter estimation Masoud Karimi-Ghartemani,
Alireza K. Ziarani 293
PART 10. ALGORITHMS, COMPUTATION 297 Problem 10.1. Root-clustering for
multivariate polynomials and robust stability analysis Pierre-Alexandre
Bliman 299 Problem 10.2. When is a pair of matrices stable? Vincent D.
Blondel, Jacques Theys, John N. Tsitsiklis 304 Problem 10.3. Freeness of
multiplicative matrix semigroups Vincent D. Blondel, Julien Cassaigne,
Juhani Karhumäki 309 Problem 10.4. Vector-valued quadratic forms in control
theory Francesco Bullo, Jorge Cortés, Andrew D. Lewis, Sonia Martínez 315
Problem 10.5. Nilpotent bases of distributions Henry G. Hermes, Matthias
Kawski 321 Problem 10.6. What is the characteristic polynomial of a signal
flow graph? Andrew D. Lewis 326 Problem 10.7. Open problems in randomized
[mu] analysis Onur Toker 330