Eur. Phys. J. B 65, 571-576 (2008)
https://doi.org/10.1140/epjb/e2008-00371-x

Control of unstable steady states in neutral time-delayed systems

¹ Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1TR, UK
² Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany

Corresponding author: ^a k.blyuss@bristol.ac.uk

Received: 2 June 2008
Revised: 6 September 2008
Published online: 27 September 2008

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.