The necessity of painless surgery and delivering an accurate dose of drug to induce anaesthesia to the patient is indubitable. Delivering a higher dose to the patient may lead to adverse effects and postoperative complications, while a lower dose obviously leads the patient to regain consciousness during the surgery and in extreme cases even to surgery failure. To overcome such complications during surgeries several research studies revolve around the design of a computer-controlled system to deliver an accurate dose of drug to induce anaesthesia. Therefore this paper aims to introduce an exact linearization of the drug administration model in anaesthesia, without losing too much information about the internal dynamics. This is realised by creating a linear map between the input and output. The control law uses this model and is designed to ensure performances of no overshoot and minimum steady-state error. The control loop is tested on a system with parametric uncertainties (related to patient intra/inter-variability). The simulation results validate the proposed approach and demonstrate its robustness.