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Stabilization of second order nonlinear equations with variable delay · arXivDesk

1606.03045Jun 9, 201610 pages, 4 figures, published in 2015 in International Journal of Control, non-autonomous second order delay differential equations, stabilization, proportional feedback, a controller with damping, derivative control, sunflower equation

Stabilization of second order nonlinear equations with variable delay

Leonid Berezansky, Elena Braverman, Lev Idels

Dynamical Systems

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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 stabilize unstable motions of the system. The delays are variable, which leads to more flexible controls permitting delay perturbations; only delay bounds are significant for stabilization by a delayed control. The results are applied to the sunflower equation which has an infinite number of equilibrium points.

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The paper addresses: Stabilization of second order nonlinear equations with variable delay.
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 stabilize unstable motions of the system.

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Author comment: 10 pages, 4 figures, published in 2015 in International Journal of Control, non-autonomous second order delay differential equations, stabilization, proportional feedback, a controller with damping, derivative control, sunflower equation