We introduce new conditions for the H-infinity synthesis of discrete-time linear parameter-varying systems in the form of linear matrix inequalities. A distinctive feature of the proposed conditions is the ability to handle variation in both the dynamics and the input matrices without resorting to dynamic augmentation or iterative procedures. We show that this new condition contains the existing poly-quadratic H-infinity synthesis result as a particular case. We also derive a corollary which shows improvement even in the stronger case of quadratic H-infinity synthesis. Additionally, we show that, surprisingly, a dynamic gain-scheduled quadratic H-infinity controller can result in inferior performance compared to a static robust controller. Numerical examples illustrate our results.