Control of near-grazing dynamics and discontinuity-induced bifurcations in piecewise-smooth dynamical systems

Sambit Misra, Harry Dankowicz

Research output: Contribution to journalArticlepeer-review


This paper develops a rigorous control paradigm for regulating the near-grazing bifurcation behavior of limit cycles in piecewise-smooth dynamical systems. In particular, it is shown that a discrete-in-time linear feedback correction to a parameter governing a state-space discontinuity surface can suppress discontinuity-induced fold bifurcations of limit cycles that achieve near-tangential intersections with the discontinuity surface. The methodology ensures a persistent branch of limit cycles over an interval of parameter values near the critical condition of tangential contact that is an order of magnitude larger than that in the absence of control. The theoretical treatment is illustrated with a harmonically excited damped harmonic oscillator with a piecewise-linear spring stiffness as well as with a piecewise-nonlinear model of a capacitively excited mechanical oscillator.

Original languageEnglish (US)
Pages (from-to)1836-1851
Number of pages16
JournalInternational Journal of Robust and Nonlinear Control
Issue number16
StatePublished - Nov 10 2010


  • delay feedback control
  • discontinuity-induced bifurcations
  • grazing bifurcations
  • piecewise-smooth dynamical systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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