Stabilisation of second-order nonlinear equations with variable delay

Leonid Berezansky, Elena Braverman, Lev Idels

Research output: Contribution to journalArticlepeer-review


For a wide class of second-order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal allows to stabilise unstable motions of the system. The delays are variable, which leads to more flexible controls permitting delay perturbations; only delay bounds are significant for stabilisation by a delayed control. The results are applied to the sunflower equation which has an infinite number of equilibrium points.

Original languageEnglish
Pages (from-to)1533-1539
Number of pages7
JournalInternational Journal of Control
Issue number8
StatePublished - 3 Aug 2015


  • a controller with damping
  • derivative control
  • non-autonomous second-order delay differential equations
  • proportional feedback
  • stabilisation
  • sunflower equation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


Dive into the research topics of 'Stabilisation of second-order nonlinear equations with variable delay'. Together they form a unique fingerprint.

Cite this