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The process of anesthesia is nonlinear with time delay and also there are some constraints which have to be considered in calculating administrative drug dosage. The controller should be enough robust in the presence of patient variability and disturbance caused by surgical stimulation. For these purposes, we present an Extended Kalman Filter (EKF) observer to estimate drug concentration in the patient's body and use this estimation in a state-space based Model of Predictive Controller (MPC) for controlling the depth of anesthesia. In this paper, we use Bispectral Index (BIS) is used as a patient consciousness index and propofol as an anesthetic agent. Performance evaluations of the proposed controller, the results have been compared with those of a PID controller. The results demonstrate that the state-space based model predictive controller provides a better robustness whether with respect to the measurement or with patient uncertainties compared to the conventional PID controller.