Stabilization of unstable steady states by variable-delay feedback control

Department of Physics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University P. O. Box 162, 1000 Skopje, Macedonia

Corresponding authors: agjurcin@iunona.pmf.ukim.edu.mk urumov@iunona.pmf.ukim.edu.mk

Received: 2 April 2008
Accepted: 16 October 2008

Abstract

We report on a significant improvement of the performance of the classical time-delayed autosynchronization method (TDAS) to control unstable steady states, by applying a time-varying delay in the TDAS control scheme in a form of a deterministic or stochastic delay modulation in a fixed interval around a nominal delay value. The successfulness of this variable-delay feedback control (VDFC) is illustrated by a numerical control simulation of the chaotic Lorenz system using three different types of time-delay modulations: a sawtooth wave, a sine wave, and a uniform random distribution. We perform a comparative analysis between the VDFC method and the standard TDAS method for a sawtooth wave modulation by analytically determining the domains of control for the generic case of an unstable fixed point of focus type.