Bleich, ME; Socolar, JES, *Stability of periodic orbits controlled by time-delay feedback*,
Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 210 no. 1-2
(1996),
pp. 87-94 .
**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.*