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In this study, the speed control of a DC motor with input delay and external disturbance is investigated. A delay-dependent memory state feedback robust predictor-based H ∞   controller that formerly has presented is utilized. Sufficient LMIs conditions provide the stabilizing gain of the predictor-based controller. The first-order model of a DC motor has been studied previously using PID and STA (super twisting algorithm) methods. However, in this paper, the delay-dependent robust H ∞   controller is used on both the first and second orders of the DC motor. Finally, the predictor-based H ∞   controller is compared to the PID controller and the common H ∞   controller as well. The simulation results show that the proposed method has been more useful and efficient.