Theoretical and experimental aspects of chaos control by time-delayed feedback

We review recent developments for the control of chaos by time-delayed feedback methods. While such methods are easily applied even in quite complex experimental context the theoretical analysis yields infinite-dimensional differential-difference systems which are hard to tackle. The essential ideas for a general theoretical approach are sketched and the results are compared to electronic circuits and to high power ferromagnetic resonance experiments. Our results show that the control performance can be understood on the basis of experimentally accessible quantities without resort to any model for the internal dynamics.