We investigate the stability of a class of dynamical systems that switch among a given finite family of hybrid systems. We propose sufficient conditions tailored to this particular type of hybrid systems which guarantee the uniform global pre-asymptotic stability (UGpAS) of a given closed set. We first assume this set to be UGpAS for each system of the family. A slow switching condition is then presented to maintain this property for the overall system. We introduce for this purpose the concept of hybrid dwell time which characterizes the length of the hybrid time intervals between two successive switching instants.
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