Enlarging the stable domain of controlled high-period oscillations with transient extended delayed feedback control

Abstract A transient extended delayed feedback control method was developed by modifying the original extended delayed feedback control method with a transient control technique to enlarge the stable domain of the controlled high-period oscillations. The control force is applied to the system only when the system is in the controlling region, which is different from the static control force of the original extended delayed feedback control. The specific control performance of the transient extended delayed feedback control was analyzed through case studies. The relationships between the stable domain of the controlled high-period oscillations and the controlling regions were obtained by calculating the largest magnitude of the Floquet multipliers. It is shown that the stable domain changes in a non-smooth manner with the variation of the controlling region. In particular, the transient extended delayed feedback control can stabilize high-period unstable oscillations in a much larger stable domain than that of the original extended delayed feedback control when the controlling region is properly chosen.