Displaying similar documents to “On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients”

Patchy Vector Fields and Asymptotic Stabilization

Fabio Ancona, Alberto Bressan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on ℝ n . We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of “patchy feedbacks” which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at...