On the Local Stabilization of Hybrid Limit Cycles in Switched Affine Systems

Most of the proposed controllers for switched affine systems are able to drive the system trajectory to a sufficiently small neighborhood of a desired state. However, the trajectory behavior in this neighborhood is not generally considered despite the fact that the system performance may be judged by its steady operation as the case of power converters. This note investigates the local stabilization of a desired limit cycle in switched affine systems using the hybrid Poincaré map approach. To this end, interesting algebraic properties of the Jacobian of the hybrid Poincaré map are firstly discussed and used for the controller design to achieve asymptotic stability conditions of the limit cycle. A dc-dc four-level power converter is considered as an illustrative example to highlight the developed results.