Chapters in this book

1. Frontmatter iii
2. Contents vii
3. Preface xiii
4. Associate Editors xv
5. Website xvii
6. PART 1. Linear Systems
7. Problem 1.1 Stability and composition of transfer functions 3
8. Problem 1.2 The realization problem for Herglotz-Nevanlinna functions 8
9. Problem 1.3 Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization? 14
10. Problem 1.4 Partial disturbance decoupling with stability 18
11. Problem 1.5 Is Monopoli’s model reference adaptive controller correct? 22
12. Problem 1.6 Model reduction of delay systems 29
13. Problem 1.7 Schur extremal problems 33
14. Problem 1.8 The elusive iff test for time-controllability of behaviours 36
15. Problem 1.9 A Farkas lemma for behavioral inequalities 40
16. Problem 1.10 Regular feedback implementability of linear differential behaviors 44
17. Problem 1.11 Riccati stability 49
18. Problem 1.12 State and first order representations 54
19. Problem 1.13 Projection of state space realizations 58
20. PART 2. Stochastic Systems
21. Problem 2.1 On error of estimation and minimum of cost for wide band noise driven systems 67
22. Problem 2.2 On the stability of random matrices 71
23. Problem 2.3 Aspects of Fisher geometry for stochastic linear systems 76
24. Problem 2.4 On the convergence of normal forms for analytic control systems 82
25. PART 3. Nonlinear Systems
26. Problem 3.1 Minimum time control of the Kepler equation 89
27. Problem 3.2 Linearization of linearly controllable systems 93
28. Problem 3.3 Bases for Lie algebras and a continuous CBH formula 97
29. Problem 3.4 An extended gradient conjecture 103
30. Problem 3.5 Optimal transaction costs from a Stackelberg perspective 107
31. Problem 3.6 Does cheap control solve a singular nonlinear quadratic problem? 111
32. Problem 3.7 Delta-Sigma modulator synthesis 114
33. Problem 3.8 Determining of various asymptotics of solutions of nonlinear time-optimal problems via right ideals in the moment algebra 117
34. Problem 3.9 Dynamics of principal and minor component flows 122
35. PART 4. Discrete Event, Hybrid Systems
36. Problem 4.1 L2-induced gains of switched linear systems 131
37. Problem 4.2 The state partitioning problem of quantised systems 134
38. Problem 4.3 Feedback control in flowshops 140
39. Problem 4.4 Decentralized control with communication between controllers 144
40. PART 5. Distributed Parameter Systems
41. Problem 5.1 Infinite dimensional backstepping for nonlinear parabolic PDEs 153
42. Problem 5.2 The dynamical Lame system with boundary control: on the structure of reachable sets 160
43. Problem 5.3 Null-controllability of the heat equation in unbounded domains 163
44. Problem 5.4 Is the conservative wave equation regular? 169
45. Problem 5.5 Exact controllability of the semi-linear wave equation 173
46. Problem 5.6 Some control problems in electromagnetics and fluid dynamics 179
47. PART 6. Stability, Stabilization
48. Problem 6.1 Copositive Lyapunov functions 189
49. Problem 6.2 The strong stabilization problem for linear time-varying systems 194
50. Problem 6.3 Robustness of transient behavior 197
51. Problem 6.4 Lie algebras and stability of switched nonlinear systems 203
52. Daniel Liberzon 208
53. Problem 6.6 Delay independent and delay dependent Aizerman problem 212
54. Problem 6.7 Open problems in control of linear discrete multidimensional systems 221
55. Problem 6.8 An open problem in adaptative nonlinear control theory 229
56. Problem 6.9 Generalized Lyapunov theory and its omega-transformable regions 233
57. Problem 6.10 Smooth Lyapunov characterization of measurement to error stability 239
58. PART 7. Controllability, Observability
59. Problem 7.1 Time for local controllability of a 1-D tank containing a fluid modeled by the shallow water equations 247
60. Problem 7.2 A Hautus test for infinite-dimensional systems 251
61. Problem 7.3 Three problems in the field of observability 256
62. Problem 7.4 Control of the KdV equation 260
63. PART 8. Robustness, Robust Control
64. Problem 8.1 H_∞-norm approximation 267
65. Problem 8.2 Non-iterative computation of optimal value in H_∞ control 271
66. Problem 8.3 Determining the least upper bound on the achievable delay margin 276
67. Problem 8.4 Stable controller coefficient perturbation in floating point implementation 280
68. PART 9. Identification, Signal Processing
69. Problem 9.1 A conjecture on Lyapunov equations and principal angles in subspace identification 287
70. Problem 9.2 Stability of a nonlinear adaptive system for filtering and parameter estimation 293
71. PART 10. Algorithms, Computation
72. Problem 10.1 Root-clustering for multivariate polynomials and robust stability analysis 299
73. Problem 10.2 When is a pair of matrices stable? 304
74. Problem 10.3 Freeness of multiplicative matrix semigroups 309
75. Problem 10.4 Vector-valued quadratic forms in control theory 315
76. Problem 10.5 Nilpotent bases of distributions 321
77. Problem 10.6 What is the characteristic polynomial of a signal flow graph? 326
78. Problem 10.7 Open problems in randomized μ analysis 330