Averaging tools for singularly perturbed hybrid systems

Singular perturbation results for a class of hybrid systems are presented. It is assumed that the fast states are restricted to a compact set and that the continuous-time boundary layer dynamics generate a well defined average vector field for the slow dynamics. This average is used to define an appropriate reduced hybrid dynamical system. Assuming forward pre-completeness for the reduced hybrid system we establish closeness of solutions between the actual and reduced hybrid systems on compact time domains. Also, if the average system is asymptotically stable (AS), we show that the actual system is semi-globally practically asymptotically stable (SGP-AS). Several examples illustrate our results and are used to compare them to prior results in the literature.