Control of unstable steady states by extended time-delayed feedback

Abstract

Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This system represents a generic model of an unstable steady state which can be found for instance in a Hopf bifurcation. In addition to the original controller design, we investigate effects of control loop latency and a bandpass filter on the domain of control. Furthermore, we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase. We present an analysis of the domain of control and support our results by numerical calculations.

11 pages, 16 figures

References in corpus (2)

• Time--delay autosynchronization of the spatio-temporal dynamics in resonant tunneling diodes
• Self-stabilization of high frequency oscillations in semiconductor superlattices by time-delay autosynchronization

Cited by in corpus (6)

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• Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback
• Stabilization of unstable steady states by variable delay feedback control
• Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback
• Control of coherence resonance in semiconductor superlattices
• Resonant control of stochastic spatio-temporal dynamics in a tunnel diode by multiple time delayed feedback