The problem of output dead-beat control with asymptotic disturbance rejection for linear discrete-time systems with disturbance input is considered. The system considered is composed of the plant to be controlled and the disturbance generator whose state vector is the disturbance input to the plant. We propose a design method of the controller which is organized by the feedback gain to stabilize the closed-loop of the plant and the compensator for the disturbance. It is shown that the proposed controller can force the output of the plant to zero and keep it zero by using the measurement output of the augmented system and the estimate of the disturbance which is obtained from the adaptive estimation process composed of an unbiased linear functional observer and an adaptive state observer. Some numerical examples show the validity of the proposed controller.
