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We investigate stability of a class of singularly perturbed systems whose slow system is a set-valued average defined via an appropriate averaging procedure of the solutions of the continuous-time boundary layer system. An approximate hybrid system consisting of this average, the projection of the jump map in the direction of the slow states and flow and jump sets from the original dynamics is shown...
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...
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