We consider methods for synthesizing robust controllers that can be directly implemented in the Internal Model Control (IMC) scheme. We show how to put H-infinity design methods into the IMC scheme to improve its robustness. These methods include one degree-of-freedom (one d.o.f.) and two degrees-of-freedom (two d.o.f.) H-infinity designs. Explicit state-space formulae for the H-infinity one d.o.f. and two d.o.f. IMC-based controllers are derived in discrete time. We show that the IMC controller solves a special H-infinity control problem, namely a disturbance feedforward control problem, and it proves robust stability against coprime factor uncertainty and with a degree of robust performance for the two d.o.f. case, in the sense of making the closed-loop system match a pre-specified reference model. A design for a glass tube production process is presented as an illustrative example.