Stabilisation of second-order nonlinear equations with variable delay

作者：Berezansky Leonid; Braverman Elena^*; Idels Lev

来源：International Journal of Control, 2015, 88(8): 1533-1539.

DOI：10.1080/00207179.2015.1009948

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

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.

• 出版日期2015-8-3