Open Problems in Mathematical Systems and Control Theory

1 Uniform asymptotic stability of linear time-varying systems.- 2 Positive system realizations.- 3 System approximation in the 2-norm.- 4 Is it possible to recognize local controllability in a finite number of differentiations?.- 5 Open problems in sequential parametric estimation.- 6 Conditions for the existence and uniqueness of optimal matrix scalings.- 7 Matrix inequality conditions for canonical factorization of rational transfer function matrices.- 8 Open problems in ?1 optimal control.- 9 Efficient neural network learning.- 10 Mechanical feedback control systems.- 11 Three problems on the decidability and complexity of stability.- 12 Simultaneous stabilization of linear systems and interpolation with rational functions.- 13 Forbidden state control synthesis for timed Petri net models.- 14 On matrix mortality in low dimensions.- 15 Entropy and random feedback.- 16 A stabilization problem.- 17 Spectral factorization of a spectral density with arbitrary delays.- 18 Lyapunov exponents and robust stabilization.- 19 Regular spectral factorizations.- 20 Convergence of an algorithm for the Riemannian SVD.- 21 Some open questions related to flat nonlinear systems.- 22 Approximation of complex ?.- 23 Spectral value sets of infinite-dimensional systems.- 24 Selection of the number of inputs and states.- 25 Input-output gains of switched linear systems.- 26 Robust stability of linear stochastic systems.- 27 Monotonicity of performance with respect to its specification in H? control.- 28 Stable estimates in equation error identification: An open problem.- 29 Elimination of latent variables in real differential algebraic systems.- 30 How conservative is the circle criterion?.- 31 On chaotic observer design.- 32 The minimal realization problem in the max-plus algebra.- 33 Input design for worst-case identification.- 34 Max-plus-times linear systems.- 35 Closed-loop identification and self-tuning.- 36 To estimate the L2-gain of two dynamic systems.- 37 Open problems in the area of pole placement.- 38 An optimal control theory for systems defined over finite rings.- 39 Re-initialization in discontinuous systems.- 40 Control-Lyapunov functions.- 41 Spectral Nevanlinna-Pick Interpolation.- 42 Phase-sensitive structured singular value.- 43 Conservatism of the standard upper bound test: Is sup$$
\left( {\bar \mu /\mu } \right)
$$ finite? Is it bounded by 2?.- 44 When does the algebraic Riccati equation have a negative semi-definite solution?.- 45 Representing a nonlinear input-output differential equation as an input-state-output system.- 46 Shift policies in QR-like algorithms and feedback control of self-similar flows.- 47 Equivalences of discrete-event systems and of hybrid systems.- 48 Covering numbers for input-output maps realizable by neural networks.- 49 A powerful generalization of the Carleson measure theorem?.- 50 Lyapunov theory for high order differential systems.- 51 Performance lower bound for a sampled-data signal reconstruction.- 52 Coprimeness of factorizations over a ring of distributions.- 53 Where are the zeros located?.