[上传完毕]Unsolved Problems in Mathematical Systems and Control Theory.pdf

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Part I, Linear systems
problem1, stability and composition of transfer functions
problem2, the realization problem for herglotz-nevanlinna functions
problem3, Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization?
problem4, Partial disturbance decoupling with stability
problem5, Is monopoli's model reference adaptive controller correct?
problem6, Model reduction of delay systems
problem7, schur extremal problems
problem8, The elusive iff test for time controllability of behaviors
problem9, A farkas lemma for behavior ineaualities
problem10, Regular feedback implementability of linear differential behaviors
problem11, Riccati stability
problem12, State and first order representations
problem13, Projection of state space realizations

Part 2, Stochastic systems
problem1, On error of estimation and minimum of cost for wide band noise driven systems
problem2, On the stability of random matrices
problem3, Aspects of fisher geomety for stochastic linear systems
problem4, On the convergence of normal forms for analytic control systems

Part 3, Nonlinear systems
problem1, Minimum time control of the Kepler equation
problem2, Linearization of linearly controllable systems
problem3, Bases for Lie algebras and a continuous CBH formula
problem4, An extended gradient conjecture
problem5, Optimal transaction costs from a Stackelberg perspective
problem6, Does cheap control solve a singular nonlinear quadratic problem?
problem7, Delta-Sigma modulator synthesis
problem8, Determining of various asymptotics of solutions of nonlinear time-optimal problems via right ideals in the moment algebra
problem9, Dynamics of principal and minor component flows

Part4, Discrete event, Hybrid systems
problem1, L2-induced gains of switched linear systems
problem2, The state partitioning problem of quantized systems
problem3, Feedback control in flowshops
problem4, Decentralized control with communication between controllers

Part5, Distributed parameter systems
problem1, Infinite dimensional backstepping for nonlinear parabolic PDEs
problem2, The dynamical Lame system with boundary control: on the structure of reachable sets
problem3, Null-controllability of the heat equation in unbounded domains
problem4, Is the conservative wave equation regular?
problem5, Exact controllability of the semilinear wave equation
problem6, Some control problems in electromagnetics and fluid dynamics

Part 6, Stability, stabilization
problem1, Copositive lyapunov function
problem2, The strong stabilization problem for linear time-varying systems
problem3, Robustness of transient behavior
problem4, Lie algebras and stability of switched nonlinear systems
problem5, Robust stability test for interval fractional order linear systems
problem6, Delay-independent and delay-dependent Aizerman problem
problem7, Open problems in control of linear discrete multidimensional systems
problem8, An open problem in adaptative nonlinear control theory
problem9, Generalized Lyapunov theory and its omega-transformable regions
problem10, Smooth Lyapunov characterization of measurement to error stability

Part 7 Controllability, Obserbability
problem1, Time for local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
problem2, A Hautus test for infinite -dimensional systems
problem3, Three problems in the field of observability
problem4, Control of the KdV equation

Part 8, Robustness, Robust control
problem1, Hinfinite norm approximaiton
problem2, Noniterative cmputation of optimal value in Hinfinite control
problem3, Determining the least upper bound on the achievable delay margin
problem4, Stable controller coefficient perturbation in floating point implementation

Part 9 , Identification, Siganl processing
problem1, A conjecture on Lyapunov equations and principal angels in subspace identification
problem2, Stability of a nonlinear adaptive system for filtering and parameter estimation

Part10, Algorithms , Computaion
problem1, Root-clustering for multivariate polynomials and robust stability analysis
problem2, When is a pair of matrices stable?
problem3, Freeness of multiplicative matrix semigroups
problem4, Vector-valued quadratic forms in cotnrol theory
problem5, Nilpotent bases of distributions
problem6, What is the characteristic polynomial of a signal flow graph?
problem7, Open problems in randomized mu analysis