Asymptotic tracking of periodic solutions using state feedback damping control

This paper considers the design of smooth state feedback controllers to track periodic solutions of control affine nonlinear systems. The objective is to show that stabilization of desired periodic solutions can be achieved by tracking a periodic reference signal using time-dependent damping feedback. The approach consists in computing an expression for a locally defined time-varying dissipative potential for the error dynamics. Following the Jurdjevic-Quinn approach, the obtained potential is then used to construct a smooth feedback controller that asymptotically stabilizes the system to the desired periodic invariant set. A numerical application to a Lotka-Volterra system is presented to illustrate the construction.