This paper deals with the maintenance phase control of general anesthesia during surgery, involving saturated input and noisy output. The objective is to maintain the patient to some given depth of hypnosis, measured by the BIS. The control law is an observer-based control, where a dead-zone observer is built in order to mitigate the presence of the output noise. The global exponential stability of the complete closed-loop system in the noise-free case is guaranteed thanks to a linear matrix inequality condition and an input-to-state property in presence of the noise is also proven. A three-steps optimization algorithm is proposed to determine the parameters of the control law and then evaluated on a patient case.