This paper addresses the gain-scheduling of separately designed controllers to form a robust linear parameter varying (LPV) controller for an LPV plant. Fast parameter variation or switching often leads to loss of stability or performance due to an inadequate gain-scheduled controller design. This paper extends a controller interpolation framework to the gain-scheduled control design problem in order to optimize the dynamic transition among controllers with respect to the quadratic H∞ performance metric. Subsequently, necessary and sufficient conditions are stated in terms of linear matrix inequalities (LMIs). In addition, the framework is also amenable to optimizing gain-scheduled control design with respect to other objectives expressible as LMIs.