A topological obstruction in a control problem

Mireille E. Broucke, Melkior Ornik, Abdol Reza Mansouri

Research output: Contribution to journalArticlepeer-review


One of the important discoveries in control theory is a topological obstruction to continuous feedback stabilization for general nonlinear control systems. In this note we describe another topological obstruction arising from a very different control problem called the reach control problem. Motivated by a classical topological obstruction for extending continuous maps on spheres, we introduce the problem of extending continuous maps on simplices. It is shown that the same condition as in the sphere case gives rise to the obstruction.

Original languageEnglish (US)
Pages (from-to)71-79
Number of pages9
JournalSystems and Control Letters
StatePublished - Oct 2017
Externally publishedYes


  • Extension problem
  • Reach control problem
  • Topological obstruction

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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