Frequency domain methods and control of complex dynamics

The paper deals with the problem of controlling complex dynamics in periodically forced systems. A general framework for the stabilization of periodic orbits based on the so-called "delayed feedback" technique is presented. We formulate the periodic orbit stabilization as an input-output L2-stability problem and employ frequency methods in the L2 setting to determine a stability bound of the periodic orbit. Although such a bound is conservative in nature, controllers achieving a larger bound exhibit a better control performance, as shown in several application examples.