Patchy vector fields and asymptotic stabilization
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Fabio Ancona, Alberto Bressan (1999)
ESAIM: Control, Optimisation and Calculus of Variations
Fabio Ancona, Alberto Bressan (2010)
ESAIM: Control, Optimisation and Calculus of Variations
This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on . 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 the origin,...
Tolstonogov, A.A. (2004)
Sibirskij Matematicheskij Zhurnal
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