Stabilizing periodic orbits of forced systems via generalized Pyragas controllers

This brief deals with the problem of designing linear time-invariant feedback controllers to stabilize unstable periodic orbits for a class of sinusoidally forced nonlinear systems. 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 rendition, 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.