This paper deals with a new strategy for the control of anesthesia taking into account the saturation of the actuator and the target interval tolerated for the depth of anesthesia during a surgery. In addition, to take into account multiple time scale dynamics in the anesthesia model, the system is re-expressed by decoupling the fast dynamics from the slow ones. These slow dynamics are then considered as disturbances for the fast system. Similarly the fast states correspond to disturbances for the slow subsystem. Taking into account the variability of the patient by using the polytopic uncertainty framework, robust control design is proposed through quasi-LMI (linear matrix inequalities) conditions. The characterization of domains of stability and invariance for both the slow and fast subsystems is provided. Then associated convex optimization issues are discussed. Finally, the theoretical conditions are evaluated on a panel of simulated patients.