The authors formulate and analyze a controller synthesis problem for a plant which must meet certain hard real-time deadlines. In this timed input-output control problem, the plant is modeled by finite timed traces. The authors provide necessary and sufficient conditions for the existence of a timed input-output controller. The results are based in part on the supervisory control theory of P.J. Ramadge and W.M. Wonham. When the plant and the closed-loop specification are represented by deterministic limited automata, the synthesis problem can be solved. The synthesis procedure and the synthesized supervisor are polynomial in the number of automata states and exponential in the timing information.>