We consider switching H∞ controllers for a class of linear parameter varying (LPV) systems scheduled along a measurable parameter trajectory. The candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable. We provide sufficient conditions to guarantee the stability of the switching LPV systems in terms of the dwell time and the average dwell time. Our results are illustrated with an example, where switching between two robust controllers is performed for an LPV system.