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Stability of periodic orbits controlled by time-delay feedback

Michael E. Bleich·Joshua E. S. Socolar
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Abstract

Extended time-delay auto-synchronization (ETDAS) is a promising technique for stabilizing unstable periodic orbits in low-dimensional dynamical systems. The technique involves continuous feedback of signals delayed by multiples of the orbit's period in a manner that is especially well-suited for fast systems and optical implementation. We show how to analyze the stability of a given implementation of ETDAS without explicit integration of time-delay equations. To illustrate the method and point out some nontrivial features of ETDAS, we obtain the domain of control for a period-one orbit of the driven, damped pendulum.

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Michael E. Bleich, Joshua E. S. Socolar. 1995-10-28. Stability of periodic orbits controlled by time-delay feedback. https://doi.org/10.1016/0375-9601(95)00827-6

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