Patchy vector fields and asymptotic stabilization

Fabio Ancona, Alberto Bressan

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


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 languageEnglish (US)
Pages (from-to)445-471
Number of pages27
JournalESAIM - Control, Optimisation and Calculus of Variations
StatePublished - Jul 1999

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


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