On local linearization of control systems

Abstract : We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at ``strongly'' singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology.
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Journal of Dynamical and Control Systems, Springer Verlag, 2009, 15 (4), pp.471-536. 〈10.1007/s10883-009-9077-9〉
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Laurent Baratchart, Jean-Baptiste Pomet. On local linearization of control systems. Journal of Dynamical and Control Systems, Springer Verlag, 2009, 15 (4), pp.471-536. 〈10.1007/s10883-009-9077-9〉. 〈inria-00087024v3〉

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