Contents

Preface

Associate Editors

Website

PART 1. LINEAR SYSTEMS

Problem 1.1. Stability and composition of transfer functions

Guillermo Fernández-Anaya, Juan Carlos Martínez-García

Problem 1.2. The realization problem for Herglotz-Nevanlinna functions

Seppo Hassi, Henk de Snoo, Eduard Tsekanovsk

Problem 1.3. Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization?

Dmitry S. Kalyuzhniy-Verbovetzky

Problem 1.4. Partial disturbance decoupling with stability

Juan Carlos Martínez-García, Michel Malabre, Vladimir Kučera

Problem 1.5. Is Monopoli’s model reference adaptive controller correct?

A. S. Morse

Problem 1.6. Model reduction of delay systems

Jonathan R. Partington

Problem 1.7. Schur extremal problems

Lev Sakhnovich

Problem 1.8. The elusive iff test for time-controllability of behaviors

Amol J. Sasane

Problem 1.9. A Farkas lemma for behavioral inequalities

A.A. (Tonny) ten Dam, J.W. (Hans) Nieuwenhuis

Problem 1.10. Regular feedback implementability of linear differential behaviors

H. L. Trentelman

Problem 1.11. Riccati stability

Erik I. Verriest

Problem 1.12. State and first order representations

Jan C. Willems

Problem 1.13. Projection of state space realizations

Antoine Vandendorpe, Paul Van Dooren

PART 2. STOCHASTIC SYSTEMS

Problem 2.1. On error of estimation and minimum of cost for wide band noise driven systems

Agamirza E. Bashirov

Problem 2.2. On the stability of random matrices

Giuseppe C. Calafiore, Fabrizio Dabbene

Problem 2.3. Aspects of Fisher geometry for stochastic linear systems

Bernard Hanzon, Ralf Peeters

Problem 2.4. On the convergence of normal forms for analytic control systems

Wei Kang, Arthur J. Krener

PART 3. NONLINEAR SYSTEMS

Problem 3.1. Minimum time control of the Kepler equation

Jean-Baptiste Caillau, Joseph Gergaud, Joseph Noailles

Problem 3.2. Linearization of linearly controllable systems

R. Devanathan

Problem 3.3. Bases for Lie algebras and a continuous CBH formula

Matthias Kawski

Problem 3.4. An extended gradient conjecture

Luis Carlos Martins Jr., Geraldo Nunes Silva

Problem 3.5. Optimal transaction costs from a Stackelberg perspective

Geert Jan Olsder

Problem 3.6. Does cheap control solve a singular nonlinear quadratic problem?

Yuri V. Orlov

Problem 3.7. Delta-Sigma modulator synthesis

Anders Rantzer

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

Problem 3.9. Dynamics of principal and minor component flows

U. Helmke, S. Yoshizawa, R. Evans, J.H. Manton, and I.M.Y. Mareels

PART 4. DISCRETE EVENT, HYBRID SYSTEMS

Problem 4.1.-induced gains of switched linear systems

João P. Hespanha

Problem 4.2. The state partitioning problem of quantized systems

Jan Lunze

Problem 4.3. Feedback control in flowshops

S.P. Sethi and Q. Zhang

Problem 4.4. Decentralized control with communication between controllers

Jan H. van Schuppen

PART 5. DISTRIBUTED PARAMETER SYSTEMS

Problem 5.1. Infinite dimensional backstepping for nonlinear parabolic PDEs

Andras Balogh, Miroslav Krstic

Problem 5.2. The dynamical Lame system with boundary control: on the structure of reachable sets

M.I. Belishev

Problem 5.3. Null-controllability of the heat equation in unbounded domains

Sorin Micu, Enrique Zuazua

Problem 5.4. Is the conservative wave equation regular?

George Weiss

Problem 5.5. Exact controllability of the semilinear wave equation

Xu Zhang, Enrique Zuazua

Problem 5.6. Some control problems in electromagnetics and fluid dynamics

Lorella Fatone, Maria Cristina Recchioni, Francesco Zirilli

PART 6. STABILITY, STABILIZATION

Problem 6.1. Copositive Lyapunov functions

M. K. Çamlibel, J. M. Schumacher

Problem 6.2. The strong stabilization problem for linear time-varying systems

Avraham Feintuch

Problem 6.3. Robustness of transient behavior

Diederich Hinrichsen, Elmar Plischke, Fabian Wirth

Problem 6.4. Lie algebras and stability of switched nonlinear systems

Daniel Liberzon

Problem 6.5. Robust stability test for interval fractional order linear systems

Ivo Petráš, YangQuan Chen, Blas M. Vinagre

Problem 6.6. Delay-independent and delay-dependent Aizerman problem

Vladimir

Problem 6.7. Open problems in control of linear discrete multidimensional systems

Li Xu, Zhiping Lin, Jiang-Qian Ying, Osami Saito, Yoshihisa Anazawa

Problem 6.8. An open problem in adaptative nonlinear control theory

Leonid S. Zhiteckij

Problem 6.9. Generalized Lyapunov theory and its omega-transformable regions

Sheng-Guo Wang

Problem 6.10. Smooth Lyapunov characterization of measurement to error stability

Brian P. Ingalls, Eduardo D. Sontag

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

Jean-Michel Coron

Problem 7.2. A Hautus test for infinite-dimensional systems

Birgit Jacob, Hans Zwart

Problem 7.3. Three problems in the field of observability

Philippe Jouan

Problem 7.4. Control of the KdV equation

Lionel Rosier

PART 8. ROBUSTNESS, ROBUST CONTROL

Problem 8.1.-norm approximation

A.C. Antoulas, A. Astolfi

Problem 8.2. Noniterative computation of optimal value in control

Ben M. Chen

Problem 8.3. Determining the least upper bound on the achievable delay margin

Daniel E. Davison, Daniel E. Miller

Problem 8.4. Stable controller coefficient perturbation in floating point implementation

Jun Wu, Sheng Chen

PART 9. IDENTIFICATION, SIGNAL PROCESSING

Problem 9.1. A conjecture on Lyapunov equations and principal angles in subspace identification

Katrien De Cock, Bart De Moor

Problem 9.2. Stability of a nonlinear adaptive system for filtering and parameter estimation

Masoud Karimi-Ghartemani, Alireza K. Ziarani

PART 10. ALGORITHMS, COMPUTATION

Problem 10.1. Root-clustering for multivariate polynomials and robust stability analysis

Pierre-Alexandre Bliman

Problem 10.2. When is a pair of matrices stable?

Vincent D. Blondel, Jacques Theys, John N. Tsitsiklis

Problem 10.3. Freeness of multiplicative matrix semigroups

Vincent D. Blondel, Julien Cassaigne, Juhani Karhumäki

Problem 10.4. Vector-valued quadratic forms in control theory

Francesco Bullo, Jorge Cortés, Andrew D. Lewis, Sonia Mart ínez

Problem 10.5. Nilpotent bases of distributions

Henry G. Hermes, Matthias Kawski

Problem 10.6. What is the characteristic polynomial of a signal flow graph?

Andrew D. Lewis

Problem 10.7. Open problems in randomized µ analysis

Onur Toker