Occurrence of big bang bifurcations in discretized sliding-mode control systems

Enric Fossas, Albert Granados

Research output: Contribution to journalJournal articleResearchpeer-review


In this work we describe the bifurcation scenario found in a general first order system when a relay based proportional control (sliding-mode control) is considered. Based on the results given in the literature, we show the occurrence of a big bang bifurcation causing the existence of an infinite number of periodic orbits near a co-dimension two bifurcation point. We also extend in a natural way the applied theoretical result for second order systems involving 2D piecewise-defined maps.
Original languageEnglish
JournalDifferential Equations and Dynamical Systems
Issue number1-2
Pages (from-to)35-43
Publication statusPublished - 2012
Externally publishedYes


  • Big bang bifurcations
  • Two-dimensional piecewise-defined maps
  • Period adding
  • Sliding-mode control
  • Relays

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