Limit cycles with chattering in relay feedback systems

Karl Henrik Johansson, Andrey E. Barabanov, Karl Johan Åström

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Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In the paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur. This chattering is analyzed in detail and conditions for approximating it by a sliding mode are derived. A result on existence of limit cycles with chattering is given, and it is shown that the limit cycles can have arbitrarily many relay switchings each period. Limit cycles with regular sliding modes are also discussed. Examples illustrate the results.
Original languageEnglish
Pages (from-to)1414-1423
JournalIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - 2002

Subject classification (UKÄ)

  • Control Engineering


  • sliding modes
  • relay control
  • oscillations
  • nonlinear dynamics
  • Discontinuous control
  • hybrid systems


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