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Title of Journal: J Dyn Diff Equat

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Abbravation: Journal of Dynamics and Differential Equations

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Kluwer Academic Publishers-Plenum Publishers

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DOI

10.1007/s10470-013-0086-y

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ISSN

1572-9222

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A Grobman–Hartman Theorem for Control Systems

Authors: Laurent Baratchart Monique Chyba JeanBaptiste Pomet
Publish Date: 2006/07/14
Volume: 19, Issue: 1, Pages: 75-107
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Abstract

We consider the problem of locally linearizing a control system via topological transformations According to 23 there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems a generic control system when viewed as a set of underdetermined differential equations parametrized by the control cannot be linearized using pointwise transformations on the state and the control values However if we allow the transformations to depend on the control at a functional level open loop transformations we are able to prove a version of the Grobman–Hartman theorem for control systems

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Other Papers In This Journal:
  1. Basic Reproduction Ratios for Periodic Compartmental Models with Time Delay
  2. Invariant Tori of Full Dimension for Second KdV Equations with the External Parameters
  3. Second Order Abstract Neutral Functional Differential Equations
  4. Complete Global and Bifurcation Analysis of a Stoichiometric Predator–Prey Model
  5. Existence of Rotating Spots with Spatially Dependent Feedback in the Plane in a Wave Front Interaction Model
  6. A Permutation Related to Non-compact Global Attractors for Slowly Non-dissipative Systems
  7. Random Attractor Associated with the Quasi-Geostrophic Equation
  8. Existence and Asymptotic Behavior of Solutions to Semilinear Wave Equations with Nonlinear Damping and Dynamical Boundary Condition
  9. A Free Boundary Problem for the Predator–Prey Model with Double Free Boundaries
  10. Stability of Solitary Waves for the Generalized Higher-Order Boussinesq Equation
  11. A Few Remarks on Partially Hyperbolic Diffeomorphisms of $${\mathbb T}^3$$ Isotopic to Anosov
  12. On The Number of Characteristic Lines for Homogeneous Vector Fields
  13. Eigenvalues of Self-Similar Solutions of the Dafermos Regularization of a System of Conservation Laws via Geometric Singular Perturbation Theory
  14. Real Analytic Quasi-Periodic Solutions with More Diophantine Frequencies for Perturbed KdV Equations
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