Oscillating delayed feedback control schemes for stabilizing equilibrium points

TL;DR

This paper introduces two oscillating delayed feedback control schemes that effectively stabilize equilibrium points in nonlinear systems, overcoming limitations of traditional delayed feedback methods.

Contribution

The paper presents two novel oscillatory delayed feedback control methods with rigorous stability proofs for nonlinear scalar systems.

Findings

Both control schemes successfully stabilize equilibrium points.

The stability regions for the control parameters are characterized.

The methods outperform traditional delayed feedback in certain scenarios.

Abstract

Limitations of the delayed feedback control and of its extended versions have been fully treated in the literature. The oscillating delayed feedback control appears as a promising scheme to overcome this problem. In this work, two methods based on oscillatory delayed feedback control schemes for the continuous time case are dealt with. For both of them, stabilization of an equilibrium point in the general non-linear scalar case is rigorously proven. Additionally, their control performance and stability parameters region are respectively studied.