Elementary state-space concepts arc used to derive a transparent solution to the H(infinity) control problem on an infinite horizon. The main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric Riccati equations with a coupling constraint. Unlike the classical parametrization in terms of linear fractional transformation, this state-space representation has a homogeneous Riccati formulation which should help to make the most of the suboptimal controller diversity. Potential applications include the design of reduced-order controllers and, more generally, the selection of suboptimal controllers to meet or optimize additional constraints.