Abstract
An odd number of real Floquet multipliers greater than unity prevents the classical time delayed feedback control from stabilizing torsion-free orbits of nonautonomous systems. This paper investigates this limitation in the context of the method of harmonic oscillators. This method aims to stabilize periodic orbits of dynamical systems through a proper coupling to a system of harmonic oscillators. The results show that the method of harmonics oscillators does not suffer from this limitation for a proper coupling condition. A practical approach of designing the coupling condition that allows stabilizing torsion-free orbits of nonautonomous systems is presented. The success of the proposed approach is demonstrated using numerical examples.
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