Towards easier realization of time-delayed feedback control of odd-number orbits

We develop generalized time-delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive Floquet exponents, which are particularly well suited for experimental realization. We construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods. In particular, it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop. Finally, we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback.