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On the Grobman-Hartman theorem for control systems

Abstract : We consider the problem of topological linearization of control systems, i.e. local equivalence to a linear controllable system via transformations that are topological but nto necessarily differentiable. On the one hand we prove that, when point-wise transformations are considered (static feedback transformations), topological linearization implies smooth linearization, at least away from singularities. On the other hand, if we allow the transformation to depend on the control at a functional level so as to define a flow (open loop transformations), we prove a version of the Grobman-Hartman theorem for control systems.
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https://hal.inria.fr/inria-00071543
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Submitted on : Tuesday, May 23, 2006 - 5:54:26 PM
Last modification on : Monday, October 14, 2019 - 3:12:02 PM
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  • HAL Id : inria-00071543, version 1

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Laurent Baratchart, Monique Chyba, Jean-Baptiste Pomet. On the Grobman-Hartman theorem for control systems. RR-5040, INRIA. 2003. ⟨inria-00071543⟩

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