Occurrence of Big Bang Bifurcations in Discretized Sliding-mode Control Systems

  • Enric Fossas
  • Albert GranadosEmail author
Original Research


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.


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


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2012

Authors and Affiliations

  1. 1.Universitat Politècnica de Catalunya, IOCBarcelonaSpain
  2. 2.Universität Stuttgart, IPVSStuttgartGermany

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