The literature presents a large number of interesting and useful results on sampled-data systems. In this paper, we deal with control design problems for this class of systems following a different route. The novelty is that the optimal H-2 and H-infinity state feedback control design problems for sampled-data linear systems are solved in a unified and direct manner through linear matrix inequalities. To this purpose, the solution to a special two-point boundary value problem is used to verify the stability and to evaluate the performance of the closed-loop system. These results are then generalised to cope with non-uniform data rates. The theory is illustrated by means of simple examples borrowed from the literature.