We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
This paper is concerned with the structure ofasymptoticallystabilizing feedbacks for a nonlinear control system on $\mathbb{R}^n$ 
. We first introduce a family of discontinuous, piecewise smooth vector fieldsand derive a number of properties enjoyed bysolutions of the corresponding O.D.E's.We then define a class of “patchy feedbacks”which are obtained by patching together a locally finitefamily of smooth controls.Our main result shows that,if a system is asymptotically controllable at the origin, thenit can be stabilized by a piecewise constantpatchy feedback control.
