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Licensed Unlicensed Requires Authentication Published by Princeton University Press 2004

Problem 6.9 Generalized Lyapunov theory and its omega-transformable regions

From the book Unsolved Problems in Mathematical Systems and Control Theory

  • Sheng-Guo Wang
https://doi.org/10.1515/9781400826155.233
From the book
Unsolved Problems in Mathematical Systems and Control Theory
Unsolved Problems in Mathematical Systems and Control Theory

Chapters in this book (68)

Frontmatter
Contents
Preface
Associate Editors
Website
PART 1. Linear Systems
Problem 1.1 Stability and composition of transfer functions
Problem 1.2 The realization problem for Herglotz-Nevanlinna functions
Problem 1.3 Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization?
Problem 1.4 Partial disturbance decoupling with stability
Problem 1.5 Is Monopoli’s model reference adaptive controller correct?
Problem 1.6 Model reduction of delay systems
Problem 1.7 Schur extremal problems
Problem 1.8 The elusive iff test for time-controllability of behaviours
Problem 1.9 A Farkas lemma for behavioral inequalities
Problem 1.10 Regular feedback implementability of linear differential behaviors
Problem 1.11 Riccati stability
Problem 1.12 State and first order representations
Problem 1.13 Projection of state space realizations
PART 2. Stochastic Systems
Problem 2.1 On error of estimation and minimum of cost for wide band noise driven systems
Problem 2.2 On the stability of random matrices
Problem 2.3 Aspects of Fisher geometry for stochastic linear systems
Problem 2.4 On the convergence of normal forms for analytic control systems
PART 3. Nonlinear Systems
Problem 3.1 Minimum time control of the Kepler equation
Problem 3.2 Linearization of linearly controllable systems
Problem 3.3 Bases for Lie algebras and a continuous CBH formula
Problem 3.4 An extended gradient conjecture
Problem 3.5 Optimal transaction costs from a Stackelberg perspective
Problem 3.6 Does cheap control solve a singular nonlinear quadratic problem?
Problem 3.7 Delta-Sigma modulator synthesis
Problem 3.8 Determining of various asymptotics of solutions of nonlinear time-optimal problems via right ideals in the moment algebra
Problem 3.9 Dynamics of principal and minor component flows
PART 4. Discrete Event, Hybrid Systems
Problem 4.1 L2-induced gains of switched linear systems
Problem 4.2 The state partitioning problem of quantised systems
Problem 4.3 Feedback control in flowshops
Problem 4.4 Decentralized control with communication between controllers
PART 5. Distributed Parameter Systems
Problem 5.1 Infinite dimensional backstepping for nonlinear parabolic PDEs
Problem 5.2 The dynamical Lame system with boundary control: on the structure of reachable sets
Problem 5.3 Null-controllability of the heat equation in unbounded domains
Problem 5.4 Is the conservative wave equation regular?
Problem 5.5 Exact controllability of the semi-linear wave equation
Problem 5.6 Some control problems in electromagnetics and fluid dynamics
PART 6. Stability, Stabilization
Problem 6.1 Copositive Lyapunov functions
Problem 6.2 The strong stabilization problem for linear time-varying systems
Problem 6.3 Robustness of transient behavior
Problem 6.4 Lie algebras and stability of switched nonlinear systems
Daniel Liberzon
Problem 6.6 Delay independent and delay dependent Aizerman problem
Problem 6.7 Open problems in control of linear discrete multidimensional systems
Problem 6.8 An open problem in adaptative nonlinear control theory
Problem 6.9 Generalized Lyapunov theory and its omega-transformable regions
Problem 6.10 Smooth Lyapunov characterization of measurement to error stability
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
Problem 7.2 A Hautus test for infinite-dimensional systems
Problem 7.3 Three problems in the field of observability
Problem 7.4 Control of the KdV equation
PART 8. Robustness, Robust Control
Problem 8.1 H∞-norm approximation
Problem 8.2 Non-iterative computation of optimal value in H∞ control
Problem 8.3 Determining the least upper bound on the achievable delay margin
Problem 8.4 Stable controller coefficient perturbation in floating point implementation
PART 9. Identification, Signal Processing
Problem 9.1 A conjecture on Lyapunov equations and principal angles in subspace identification
Problem 9.2 Stability of a nonlinear adaptive system for filtering and parameter estimation
PART 10. Algorithms, Computation
Problem 10.1 Root-clustering for multivariate polynomials and robust stability analysis
Problem 10.2 When is a pair of matrices stable?
Problem 10.3 Freeness of multiplicative matrix semigroups
Problem 10.4 Vector-valued quadratic forms in control theory
Problem 10.5 Nilpotent bases of distributions
Problem 10.6 What is the characteristic polynomial of a signal flow graph?
Problem 10.7 Open problems in randomized μ analysis
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