Control of unstable steady states by long delay feedback

Serhiy Yanchuk, Matthias Wolfrum, Philipp Hövel, and Eckehard Schöll
Phys. Rev. E 74, 026201 – Published 2 August 2006

Abstract

We present an asymptotic analysis of time-delayed feedback control of steady states for large delay time. By scaling arguments, and a detailed comparison with exact solutions, we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type. Insight into the control mechanism is gained by analyzing the eigenvalue spectrum, which consists of a pseudocontinuous spectrum and up to two strongly unstable eigenvalues. Although the standard control scheme generally fails for large delay, we find that if the uncontrolled system is sufficiently close to its instability threshold, control does work even for relatively large delay times.

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  • Received 11 April 2006

DOI:https://doi.org/10.1103/PhysRevE.74.026201

©2006 American Physical Society

Authors & Affiliations

Serhiy Yanchuk1,2, Matthias Wolfrum1, Philipp Hövel3, and Eckehard Schöll3

  • 1Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany
  • 2Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany
  • 3Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany

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Issue

Vol. 74, Iss. 2 — August 2006

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