On optimal stabilization of periodic orbits via time delayed feedback control

The paper considers the problem of designing time delayed feedback controll ers to stabilize unstable periodic orbits of a class of sinusoidally forced nonlinear systems. This problem is formulated as an absolute stability pro blem of a linear periodic feedback system, in order to employ the well-know n circle criterion. In particular, once a single test is verified by an uns table periodic orbit of the chaotic system, our approach directly provides a procedure for designing the optimal stabilizing controller, i.e. the one ensuring the largest obtainable stability bounds. Even if the circle criter ion provides a sufficient condition for stability and therefore the obtaine d stability bounds are conservative in nature, several examples, as the one presented in this paper, show that the performance of the designed control ler is quite satisfactory in comparison with different approaches.