Existing control theory for linear parameter-varying systems uses a uniform-in-the-parameters upper bound (a constant scalar) on the induced-L/sub 2/ norm. In this paper, this constant is generalized to a function of the parameters; the performance criterion generalizes to an integral quadratic constraint and implies a norm bound that depends naturally on the real-time parameter trajectory. As in existing theory, the synthesis problem reduces to convex optimization involving linear matrix inequalities. A motivating example, gain-scheduled flight control of the F-16 VISTA, demonstrates the flexibility gained by incorporating the new performance criterion.