Control of unstable steady states by time-delayed feedback methods

TL;DR

This paper demonstrates that time-delayed feedback control can stabilize unstable steady states, extending its application from periodic orbits to fixed points, with analytical insights into the effects of filtering and latency.

Contribution

It introduces a novel application of time-delayed feedback methods for stabilizing unstable steady states and provides an analytical framework using the Lambert function.

Findings

Time-delayed feedback can stabilize unstable steady states.

Filtering and latency affect control stability.

Analytical solutions using Lambert function are derived.

Abstract

We show that time-delayed feedback methods, which have successfully been used to control unstable periodic ortbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the Lambert function and discuss effects of both a low-pass filter included in the control loop and non-zero latency times associated with the generation and injection of the feedback signal.