Global stabilization for systems evolving on manifolds

M. Malisoff, M. Krichman, E. Sontag

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the "sample and hold" sense introduced by Clarke, Ledyaev, Sontag, and Subbotin (CLSS). We generalize their theorem which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds with respect to actuator errors, under small observation noise.

Original languageEnglish (US)
Pages (from-to)161-184
Number of pages24
JournalJournal of Dynamical and Control Systems
Issue number2
StatePublished - Apr 2006

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Algebra and Number Theory
  • Numerical Analysis
  • Control and Optimization


  • Asymptotic controllability
  • Control systems on manifolds
  • Input-to-state stabilization


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