Unsolved Problems in Mathematical Systems and Control Theory /
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 refere...
| Other Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, N.J. :
Princeton University Press,
c2004
Princeton, N.J. : ©2004 Princeton, N.J. : [2004] |
| Edition: | Course Book |
| Subjects: |
Table of Contents:
- Preface; Associate Editors; Website; PART 1. LINEAR SYSTEMS; PART 2. STOCHASTIC SYSTEMS; PART 3. NONLINEAR SYSTEMS; PART 4. DISCRETE EVENT, HYBRID SYSTEMS; PART 5. DISTRIBUTED PARAMETER SYSTEMS; PART 6. STABILITY, STABILIZATION; PART 7. CONTROLLABILITY, OBSERVABILITY; PART 8. ROBUSTNESS, ROBUST CONTROL; PART 9. IDENTIFICATION, SIGNAL PROCESSING; PART 10. ALGORITHMS, COMPUTATION
- 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
- Frontmatter
- Contents
- Preface
- Associate Editors
- Website
- 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
- 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.
- 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.
- 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.
- 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
- 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.
- 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
- Problem 8.1 H / Antoulas, A. C. ; Astolfi, A.
- Problem 8.2 Non-iterative computation of optimal value in H / 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
- 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.
- 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