STABILITY OF PERIODIC-ORBITS CONTROLLED BY TIME-DELAY FEEDBACK

Extended time-delay auto-synchronization (ETDAS) is a promising techni que for stabilizing unstable periodic orbits in low-dimensional dynami cal systems. The technique involves continuous feedback of signals del ayed 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 ex plicit integration of time-delay equations. To illustrate the method a nd point out some nontrivial features of ETDAS, we obtain the domain o f control for a period-one orbit of the driven, damped pendulum.