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This report 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 modeling 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 closely match those of the original analogously controlled continuous time uncertain systems.