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A model is developed for digital control systems with deadbeat unit step response. Deadbeat systems with state feedback and state compensation configurations are synthesised based on the developed model. For plants with inaccessible states, a linear state transformation technique is introduced to obtain deadbeat output compensation design. The state feedback law presented in this paper for a deadbeat controller can be combined with the pole placement technique for a deadbeat observer to solve the observer-controller problems. A practical study that compares various designs is made from the point of view of parameter sensitivity.