Abstract
This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on ℝn. 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, then it can be stabilized by a piecewise constant patchy feedback control.
Original language | English (US) |
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Pages (from-to) | 445-471 |
Number of pages | 27 |
Journal | ESAIM - Control, Optimisation and Calculus of Variations |
Volume | 4 |
DOIs | |
State | Published - Jul 1999 |
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics