This paper focus on model predictive control (MPC) design in the context of sampled-data control systems with full-state measurements. It is shown that recent results on this area can be successfully generalized to cope with sampled-data MPC. The open-loop plant is subjected to polytopic parameter uncertainty and at sampling times a controlled output variable satisfies a set of convex constraints. A guaranteed H2 performance index with infinity horizon is minimized such as the feedback control preserves asymptotic stability and feasibility. The design conditions are expressed though differential linear matrix inequalities (DLMIs). Continuous-time systems are treated with no kind of discrete-time modeling approximation. Comparisons with classical methods from the literature dealing with continuous-time systems are presented and discussed. Examples are included for illustration.