PBC-based pulse stabilization of periodic orbits

•We give a rigorous approach to periodic control of periodic discrete systems.•Stability domains help to choose a suitable control for every particular application.•Destabilizing bifurcations are prevented.•We give applications for biological and physical models.

We investigate prediction based schemes to stabilize periodic solutions to potentially chaotic systems of periodic difference equations using pulses at times being a multiple of the period. By introducing the concept of a stability domain, we obtain precise information on the possibility to stabilize given solutions, to avoid destabilizing bifurcations, as well as on the magnitude of the required control.