Abstarct: The thesis proposes a nonlinear optimal control method for the administered infusion of insulin, aiming at regulation of patients’ blood glucose levels. The dynamic model of blood glucose concentration which receives as control input the insulin’s infusion rate, undergoes approximate linearization through Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization takes place round a temporary equilibrium which is updated at each iteration of the control method and which is defined by the last value of the system’s state vector and the last value of the control inputs vector exerted on it. For the linearized model, a robust H-infinity feedback controller is designed. To find the feedback control gain of the controller, an algebraic Riccati equation is solved at each iteration of the control algorithm. Through Lyapunov stability analysis it is first proven that the control loop satisfies the H-infinity tracking performance criterion, which signifies elevated robustness to model uncertainty and external perturbations. Moreover, the global asymptotic stability of the control loop is proven. The proposed control method can contribute to the treatment of diabetes patients and to blood glucose levels regulation in patients of intensive care units.