A new method for digital model conversion of a continuous-time uncertain system and a new digital redesign method for robust control of a sampled-data uncertain system are presented. The concept of the principle of equivalent areas together with interval arithmetic is utilised for finding the discrete-time uncertain model and the digital robust control law from the continuous-time uncertain state equation and the analogue robust control law, respectively. Using the newly digitally redesigned controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match those of the original analogously controlled continuous-time uncertain systems for a relatively longer sampling period.