Mimicking the medical practice, this paper deals with the control of hypnosis during a surgical intervention thanks to a switched control strategy. The key idea consists in starting with an initial minimum time control for the induction phase followed by a dynamic output feedback for the maintenance phase. The objective during the first phase is to bring the patient from its awake state to a final state corresponding to some given depth of hypnosis, measured by the BIS, within a minimum time. Then, once the patient state is close to the desired target, the control is switched to a dynamic output feedback ensuring that the BIS stays in a given interval taking into account the saturation of the actuator and the multi-time scale dynamics in the anesthesia model. Positivity of the system is also preserved thanks to the use of input saturation and state constraints. The stability of the switched control strategy is addressed and the theoretical conditions are evaluated on different case studies.