Robust dynamic output design most often relies on nonconvex problems. This is precisely the case with linear parameter-varying (LPV) control when the measured varying parameters do not exactly fit the real ones. This paper provides a solution in the convex programming framework with the use of linear matrix inequality (LMI) solvers in the case of polytopic parameter dependence. A bounded uncertainty set is defined from the difference between the measured and the true parameters from which LMI stabilization and performance conditions are obtained after bounding. As a desired property, the proposed conditions reduce to the classical LPV ones whenever the true parameters are available for control synthesis.