Résumé : The most general H control problem is solved by elementary state-space manipulations. Here the characterization of feasible closed-loop gains g is in terms of Riccati inequalities rather than equations. This allows treatment within a single framework of both regular and singular continuous - or discrete - time H problems. An interesting by-product of this approach is a convex state-space parametrization of all H suboptimal controllers, including reduced-order ones. Here the free parameters are pairs of positive definite matrices solving the Riccati inequalities and satisfying some coupling constraint. Such pairs form a convex set and given any of them, the controller reconstruction amounts to solving a linear matrix inequality (LMI). Applications of these results to the improvement of classical H design techniques are discussed.