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For a linear parameter-varying (LPV) plant with a large parameter variation region, it is often conservative to design a single LPV controller over the entire parameter space. This paper studies the control design of switched LPV systems using multiple parameter-dependent Lyapunov functions to improve performance and enhance design flexibility. Two autonomous switching logics, hysteresis switching and switching with average dwell time, are discussed. The control synthesis conditions for both switching logics are formulated, which are generally non-convex but can be convexified under certain conditions. The proposed switched LPV control schemes are applied to a magnetic bearing problem to demonstrate its advantages over existing LPV control approach.