Control of unstable steady states in neutral time-delayed systems

TL;DR

This paper analyzes how time-delayed feedback control can stabilize unstable steady states in neutral delay differential equations, deriving conditions for stability and exploring parameter regions for successful control.

Contribution

It provides an analytic expression for the stabilizing control strength in terms of system parameters and delays, advancing understanding of control in neutral delay systems.

Findings

Derived an explicit formula for control strength

Identified parameter regions for successful stabilization

Validated results through theoretical and numerical analysis

Abstract

We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between the control strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can successfully stabilize an otherwise unstable steady state.