Stabilization for a class of minimum phase hybrid systems under an average dwell-time constraint

We consider the class of nonlinear systems in normal form with unitary relative degree whose zero and output dynamics are affected by state jumps fulfilling an average dwell-time constraint. Under a minimum-phase assumption requiring the existence of a compact set which is globally pre-asymptotically stable for the hybrid zero dynamics, we show how to design continuous, global state- and semiglobal output-feedback control laws. The proposed design methodology extends to the considered class of hybrid systems well-known design techniques for robustly stabilizing the class of continuous-time minimum-phase nonlinear systems having unitary relative degree. Examples are given to show the usefulness of the technical result.