Stabilisation of second-order nonlinear equations with variable delay

Leonid Berezansky; Elena Braverman; Lev Idels

doi:10.1080/00207179.2015.1009948

Stabilisation of second-order nonlinear equations with variable delay

Leonid Berezansky, Elena Braverman, Lev Idels

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1533-1539
Number of pages	7
Journal	International Journal of Control
Volume	88
Issue number	8
DOIs	https://doi.org/10.1080/00207179.2015.1009948
State	Published - 3 Aug 2015

Keywords

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

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10.1080/00207179.2015.1009948

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AB - 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.

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Stabilisation of second-order nonlinear equations with variable delay

Abstract

Keywords

ASJC Scopus subject areas

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