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Unsolved Problems in Mathematical Systems and Control Theory - Vincent D. Blondel

Unsolved Problems in Mathematical Systems and Control Theory

By: Vincent D. Blondel (Editor), Alexandre Megretski (Editor)

Hardcover Published: 26th July 2004
ISBN: 9780691117485
Number Of Pages: 334
For Ages: 22+ years old

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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.

Industry Reviews

"This is an extremely important book that presents, in a clear way, many important and stimulating mathematical problems in systems and control. It will be an important reference for both researchers and people outside the field."--William W. Hager, University of Florida
"This book covers a wide range of systems from linear to nonlinear, deterministic to stochastic, finite dimensional to infinite dimensional, and so on. It includes at least some set of problems that will interest any researcher in the field."--Kemin Zhou, Louisiana State University

Prefacep. xiii
Associate Editorsp. xv
Websitep. xvii
Linear Systemsp. 1
Stability and composition of transfer functionsp. 3
The realization problem for Herglotz-Nevanlinna functionsp. 8
Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization?p. 14
Partial disturbance decoupling with stabilityp. 18
Is Monopoli''s model reference adaptive controller correct?p. 22
Model reduction of delay systemsp. 29
Schur extremal problemsp. 33
The elusive iff test for time-controllability of behaviorsp. 36
A Farkas lemma for behavioral inequalitiesp. 40
Regular feedback implementability of linear differential behaviorsp. 44
Riccati stabilityp. 49
State and first order representationsp. 54
Projection of state space realizationsp. 58
Tochastic Systemsp. 65
On error of estimation and minimum of cost for wide band noise driven systemsp. 67
On the stability of random matricesp. 71
Aspects of Fisher geometry for stochastic linear systemsp. 76
On the convergence of normal forms for analytic control systemsp. 82
Nonlinear Systemsp. 87
Minimum time control of the Kepler equationp. 89
Linearization of linearly controllable systemsp. 93
Bases for Lie algebras and a continuous CBH formulap. 97
An extended gradient conjecturep. 103
Optimal transaction costs from a Stackelberg perspectivep. 107
Does cheap control solve a singular nonlinear quadratic problem?p. 111
Delta-Sigma modulator synthesisp. 114
Determining of various asymptotics of solutions of nonlinear time-optimal problems via right ideals in the moment algebrap. 117
Dynamics of principal and minor component flowsp. 122
Discrete Event, Hybrid Systemsp. 129
L 2 -induced gains of switched linear systemsp. 131
The state partitioning problem of quantized systemsp. 134
Feedback control in flowshopsp. 140
Decentralized control with communication between controllersp. 144
Distributed Parameter Systemsp. 151
Infinite dimensional backstepping for nonlinear parabolic PDEsp. 153
The dynamical Lame system with boundary control: on the structure of reachable setsp. 160
Null-controllability of the heat equation in unbounded domains
Is the conservative wave equation regular?p. 169
Exact controllability of the semilinear wave equationp. 173
Some control problems in electromagnetics and fluid dynamicsp. 179
Stability, Stabilization
Copositive Lyapunov functionsp. 189
The strong stabilization problem for linear time-varying systemsp. 194
Robustness of transient behaviorp. 197
Lie algebras and stability of switched nonlinear systemsp. 203
Robust stability test for interval fractional order linear systemsp. 208
Delay-independent and delay-dependent Aizerman problemp. 212
Open problems in control of linear discrete multidimensional systemsp. 221
An open problem in adaptative nonlinear control theoryp. 229
Generalized Lyapunov theory and its omega-transformable regionsp. 233
Smooth Lyapunov characterization of measurement to error stabilityp. 239
Controllability, Observabilityp. 245
Time for local controllability of a 1-D tank containing a fluid modeled by the shallow water equationsp. 247
A Hautus test for infinite-dimensional systemsp. 251
Three problems in the field of observabilityp. 256
Control of the KdV equationp. 260
Robustness, Robust Control
H [infinity] -norm approximationp. 267
Noniterative computation of optimal value in H [infinity] Controlp. 271
Determining the least upper bound on the achievable delay marginp. 276
Stable controller coefficient perturbation in floating point implementationp. 280
Identification, Signal Processingp. 285
A conjecture on Lyapunov equations and principal angles in sub-space identificationp. 287
Stability of a nonlinear adaptive system for filtering and parameter estimationp. 293
Algorithms, Computationp. 297
Root-clustering for multivariate polynomials and robust stability analysisp. 299
When is a pair of matrices stable?p. 304
Freeness of multiplicative matrix semigroupsp. 309
Vector-valued quadratic forms in control theoryp. 315
Nilpotent bases of distributionsp. 321
What is the characteristic polynomial of a signal flow graph?p. 326
Open problems in randomized [mu] analysisp. 330
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691117485
ISBN-10: 0691117489
Audience: Tertiary; University or College
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 334
Published: 26th July 2004
Country of Publication: US
Dimensions (cm): 24.08 x 16.36  x 2.82
Weight (kg): 0.64