Modern engineering problems often have complicated uncertain dynamics that are difficult to accurately model; but data describing these effects can be measured. This paper proposes a data-driven robust controller synthesis approach for linear parameter varying (LPV) systems. It uses an iterative synthesis approach separated into a nominal synthesis and robust performance analysis step. It uses quadratic constraints (QC) to re-formulate the induced L2-norm analysis step with data driven linear matrix inequalities (LMI). The approach is applied to the controller synthesis for a satellite with nonlinear sloshing dynamics. The resulting controller demonstrates better attitude control performance than a nominal controller.