This paper presents a new digital redesign method for robust control of a sampled-data uncertain system using an observer-based digital controller. The multiple-segment trapezoidal rule together with interval arithmetic is utilized to find a digital interval model of the original continuous-time uncertain system. A dual concept of the digital interval modelling, which captures the intersample states of the original continuous-time uncertain system is used to discretize a predesigned continuous-time state-feedback robust controller so that the states of the digitally controlled continuous-time uncertain system closely match those of the original analogously controlled continuous-time uncertain system. A discrete-time observer is constructed from the original continuous-time observer such that the estimated states of the redesigned discrete-time observer match those of the original continuous-time observer at the sampling instants. Using the newly digitally redesigned observer-based controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systems are able to match closely those of the original analogously controlled continuous-time uncertain systems.