Unsolved problems in mathematical systems and control theory / edited by Vincent D. Blondel, Alexandre Megretski.

Format:

Book

Contributor:

Blondel, Vincent.

Megretski, Alexandre.

Language:

English

Subjects (All):

System analysis.

Control theory.

Physical Description:

1 online resource (351 p.)

Edition:

Course Book

Place of Publication:

Princeton, N.J. : Princeton University Press, c2004.

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Contents

Preface

Associate Editors

Website

PART 1. Linear Systems

Problem 1.1 Stability and composition of transfer functions / Fernández-Anaya, G. / Martínez-García, J. C.

Problem 1.2 The realization problem for Herglotz-Nevanlinna functions / Hassi, Seppo / de Snoo, Henk / Tsekanovskĭ, Eduard

Problem 1.3 Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization? / Kalyuzhniy-Verbovetzky, Dmitry S.

Problem 1.4 Partial disturbance decoupling with stability / Martínez-García, J. C. / Malabre, M. / Kučera, V.

Problem 1.5 Is Monopoli's model reference adaptive controller correct? / Morse, A. S.

Problem 1.6 Model reduction of delay systems / Partington, Jonathan R.

Problem 1.7 Schur extremal problems / Sakhnovich, Lev

Problem 1.8 The elusive iff test for time-controllability of behaviours / Sasane, Amol

Problem 1.9 A Farkas lemma for behavioral inequalities / ten Dam, A. A. (Tonny) / Nieuwenhuis, J.W. (Hans)

Problem 1.10 Regular feedback implementability of linear differential behaviors / Trentelman, H. L.

Problem 1.11 Riccati stability / Verriest, Erik I.

Problem 1.12 State and first order representations / Willems, Jan C.

Problem 1.13 Projection of state space realizations / Vandendorpe, Antoine / Van Dooren, Paul

PART 2. Stochastic Systems

Problem 2.1 On error of estimation and minimum of cost for wide band noise driven systems / Bashirov, Agamirza E.

Problem 2.2 On the stability of random matrices / Calafiore, Giuseppe / Dabbene, Fabrizio

Problem 2.3 Aspects of Fisher geometry for stochastic linear systems / Hanzon, Bernard / Peeters, Ralf

Problem 2.4 On the convergence of normal forms for analytic control systems / Kang, Wei / Krener, Arthur J.

PART 3. Nonlinear Systems

Problem 3.1 Minimum time control of the Kepler equation / Caillau, Jean-Baptiste / Gergaud, Joseph / Noailles, Joseph

Problem 3.2 Linearization of linearly controllable systems / Devanathan, R.

Problem 3.3 Bases for Lie algebras and a continuous CBH formula / Kawski, Matthias

Problem 3.4 An extended gradient conjecture / Martins, Luiz Carlos / Silva, Geraldo Nunes

Problem 3.5 Optimal transaction costs from a Stackelberg perspective / Olsder, Geert Jan

Problem 3.6 Does cheap control solve a singular nonlinear quadratic problem? / Orlov, Yuri V.

Problem 3.7 Delta-Sigma modulator synthesis / Rantzer, Anders

Problem 3.8 Determining of various asymptotics of solutions of nonlinear time-optimal problems via right ideals in the moment algebra / Sklyar, G. M. / Ignatovich, S. Yu.

Problem 3.9 Dynamics of principal and minor component flows / Helmke, U. / Yoshizawa, S. / Evans, R. / Manton, J.H. / Mareels, I.M.Y.

PART 4. Discrete Event, Hybrid Systems

Problem 4.1 L2-induced gains of switched linear systems / Hespanha, João P.

Problem 4.2 The state partitioning problem of quantised systems / Lunze, Jan

Problem 4.3 Feedback control in flowshops / Sethi, S. P. / Zhang, Q.

Problem 4.4 Decentralized control with communication between controllers / van Schuppen, Jan H.

PART 5. Distributed Parameter Systems

Problem 5.1 Infinite dimensional backstepping for nonlinear parabolic PDEs / Balogh, Andras / Krstic, Miroslav

Problem 5.2 The dynamical Lame system with boundary control: on the structure of reachable sets / Belishev, M. I.

Problem 5.3 Null-controllability of the heat equation in unbounded domains / Micu, Sorin / Zuazua, Enrique

Problem 5.4 Is the conservative wave equation regular? / Weiss, George

Problem 5.5 Exact controllability of the semi-linear wave equation / Zhang, Xu / Zuazua, Enrique

Problem 5.6 Some control problems in electromagnetics and fluid dynamics / Fatone, Lorella / Recchioni, Maria Cristina / Zirilli, Francesco

PART 6. Stability, Stabilization

Problem 6.1 Copositive Lyapunov functions / Çamlıbel, M. K. / Schumacher, J. M.

Problem 6.2 The strong stabilization problem for linear time-varying systems / Feintuch, Avraham

Problem 6.3 Robustness of transient behavior / Hinrichsen, Diederich / Plischke, Elmar / Wirth, Fabian

Problem 6.4 Lie algebras and stability of switched nonlinear systems / Liberzon, Daniel

Daniel Liberzon / Petráš, Ivo / Chen, Yang Quan / Vinagre, Blas M.

Problem 6.6 Delay independent and delay dependent Aizerman problem / Răsvan, Vladimir

Problem 6.7 Open problems in control of linear discrete multidimensional systems / Xu, Li / Lin, Zhiping / Ying, Jiang-Qian / Saito, Osami / Anazawa, Yoshihisa

Problem 6.8 An open problem in adaptative nonlinear control theory / Zhiteckij, Leonid S.

Problem 6.9 Generalized Lyapunov theory and its omega-transformable regions / Wang, Sheng-Guo

Problem 6.10 Smooth Lyapunov characterization of measurement to error stability / Ingalls, Brian P. / Sontag, Eduardo D.

PART 7. Controllability, Observability

Problem 7.1 Time for local controllability of a 1-D tank containing a fluid modeled by the shallow water equations / Coron, Jean-Michel

Problem 7.2 A Hautus test for infinite-dimensional systems / Jacob, Birgit / Zwart, Hans

Problem 7.3 Three problems in the field of observability / Jouan, Philippe

Problem 7.4 Control of the KdV equation / Rosier, Lionel

PART 8. Robustness, Robust Control

Problem 8.1 H∞-norm approximation / Antoulas, A. C. / Astolfi, A.

Problem 8.2 Non-iterative computation of optimal value in H∞ control / Chen, Ben M.

Problem 8.3 Determining the least upper bound on the achievable delay margin / Davison, Daniel E. / Miller, Daniel E.

Problem 8.4 Stable controller coefficient perturbation in floating point implementation / Wu, Jun / Chen, Sheng

PART 9. Identification, Signal Processing

Problem 9.1 A conjecture on Lyapunov equations and principal angles in subspace identification / De Cock, Katrien / De Moor, Bart

Problem 9.2 Stability of a nonlinear adaptive system for filtering and parameter estimation / Karimi-Ghartemani, Masoud / Ziarani, Alireza K.

PART 10. Algorithms, Computation

Problem 10.1 Root-clustering for multivariate polynomials and robust stability analysis / Bliman, Pierre-Alexandre

Problem 10.2 When is a pair of matrices stable? / Blondel, Vincent D. / Theys, Jacques / Tsitsiklis, John N.

Problem 10.3 Freeness of multiplicative matrix semigroups / Blondel, Vincent D. / Cassaigne, Julien / Karhumäki, Juhani

Problem 10.4 Vector-valued quadratic forms in control theory / Bullo, Francesco / Cortés, Jorge / Lewis, Andrew D. / Martínez, Sonia

Problem 10.5 Nilpotent bases of distributions / Hermes, Henry G. / Kawski, Matthias

Problem 10.6 What is the characteristic polynomial of a signal flow graph? / Lewis, Andrew D.

Problem 10.7 Open problems in randomized μ analysis / Toker, Onur

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786612087325

9781282087323

1282087320

9781400826155

1400826152

OCLC:

367684332