Stabilization of oscillations through backstepping in high-dimensional systems

This note introduces a method for obtaining stable and robust self-sustained oscillations in a class of single input nonlinear systems of dimension n≥2. The oscillations are associated to a limit cycle that is produced in a second-order subsystem by means of an appropriate feedback law. Then, the controller is extended to the full system by a backstepping procedure. It is shown that the closed-loop system turns out to be generalized Hamiltonian and that the limit cycle can be thought as born in a Hopf bifurcation after moving a parameter.