Transient behavior in systems with time-delayed feedback

TL;DR

This paper studies how long it takes for control to stabilize steady states in systems with time-delayed feedback, optimizing transient times through analytical and numerical methods.

Contribution

It introduces an analytical and numerical approach to minimize transient times in time-delayed feedback control systems, highlighting the influence of feedback gain and delay.

Findings

Transient time scales algebraically with system parameters.

Optimal feedback gain reduces transient times effectively.

Numerical simulations confirm analytical predictions.

Abstract

We investigate the transient times for the onset of control of steady states by time-delayed feedback. The optimization of control by minimising the transient time before control becomes effective is discussed analytically and numerically, and the competing influences of local and global features are elaborated. We derive an algebraic scaling of the transient time and confirm our findings by numerical simulations in dependence on feedback gain and time delay.