We consider the design ofH∞optimal discrete-time (digital) controllers in continuous-time systems. An apparent difficulty, especially in utilizing moderntransform-domainanalysis in this context, stems from the absence of an appropriate (transfer function) model for the hybrid-time (discrete and continuous) closed-loop system. This difficulty is overcome through the introduction of an equivalent difference-equation model for the continuous-time system, with distributed inputs and outputs; equivalence being in the sense that the continuous-and discrete-time inputs and outputs are essentially identical. Using the interplay between the discrete and the continuous time models, solutions of the well-known purely continuous-time and purely discrete-time standard problems extend to solutions of the problem at hand. They comprise Riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed-loop induced input-output norm, and parameterization of compensators. We consider a general setting that includes as particular instances both the case where the sensor's analog-to-digital (A/D) convertor and the control-hold (D/A) component are predetermined and cases where the design of either or both of these elements is part of the overall problem.