A generic classification of time-optimal planar stabilizing feedbacks

A. Bressan, B. Piccoli

Research output: Contribution to journalArticle

35 Scopus citations


Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335-371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto.

Original languageEnglish (US)
Pages (from-to)12-32
Number of pages21
JournalSIAM Journal on Control and Optimization
Issue number1
StatePublished - Jan 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


  • Regular synthesis
  • Time-optimal control
  • Two-dimensional system

Fingerprint Dive into the research topics of 'A generic classification of time-optimal planar stabilizing feedbacks'. Together they form a unique fingerprint.

  • Cite this