A generic classification of time-optimal planar stabilizing feedbacks

Alberto Bressan, B. Piccoli

Research output: Contribution to journalArticlepeer-review

39 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 1 1998

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


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