Stabilizing periodic orbits of forced systems via generalized Pyragas controllers

The problem of designing linear time-invariant feedback controllers to stabilize unstable periodic orbits for a class of sinusoidally forced nonlinear systems is considered. Exploiting the classical circle criterion, a sufficient condition for the stabilization of unstable periodic solutions is derived for a class of controllers that generalizes the time delayed one proposed by Pyragas, Based on this condition, a technique for designing optimal controllers is proposed. The validity of the technique and the performance of the designed controllers are illustrated via one example concerning the forced Duffing oscillator.