Controller design for improving the degree of stability of periodic solutions in forced nonlinear systems

The problem of local exponential stability of periodic orbits in a general class of forced nonlinear systems is considered. A criterion for designing a finite dimensional linear time invariant controller that improves the degree of local exponential stability with respect to the uncontrolled case is provided. Such a criterion is based on a well-known condition for exponential stability of linear time varying systems, that is suitably tailored to our periodic setting. An application example is presented to illustrate the improvement on the transient behavior of the periodic orbits that is provided by the designed controller.