Virtual orbits and two-parameter bifurcation analysis in ZAD-controled buck-converter

Viktor Avrutin, Enric Fossas, Albert Granados, Michael Schanz

Research output: Contribution to journalJournal articleResearchpeer-review


Based on a recently obtained Lemma about periodic orbits in linear systems with a piecewise-linear non-autonomous periodic control, we describe analytically the bifurcation structures in a ZAD-controlled buck converter. This analytical description shows that the period doubling bifurcation in this system may be both subcritical or supercritical. Considering virtual orbits we show how a saddle-node bifurcation becomes feasible and how it is destroyed at a new codimension-2 bifurcation point, where the subcritical period doubling bifurcation becomes supercritical. We also show that this phenomenon does not take place when the error surface in the ZAD conditions piecewise-linear defined.
Original languageEnglish
JournalNonlinear Dynamics
Issue number1
Pages (from-to)19-33
Publication statusPublished - 2011
Externally publishedYes


  • Non-smooth systems
  • Bifurcations
  • Virtual orbits
  • Zero average dynamics
  • Control
  • Power electronics


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