Unsolved Problems in Mathematical Systems and Control Theory

Name: Unsolved Problems in Mathematical Systems and Control Theory
Brand: Princeton University Press
Price: 122.75 AUD

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

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Hardcover | 5 October 2004

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Hardcover
334 Pages

Age
22+

Dimensions(cm)
23.4 x 15.2 x 3.18

Hardcover

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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

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

Unsolved Problems in Mathematical Systems and Control Theory

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Hardcover

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