Local sampled-data control of the glucose-insulin system

In this work we consider the local sampled-data stabilization of human plasma glycemia. It is proved theoretically that the implementation by sampling and holding, for suitable small sampling period, of a state feedback which is shown in the literature to yield local stabilization when applied in a continuous time basis, yields local practical stabilization, with arbitrarily small final target ball. The model of the system is given by a nonlinear retarded functional differential equation and the above state feedback is provided by standard tools of differential geometry for time-delay systems. The proposed theoretical result proves an important property for the digital implementation of the controller, which has been shown in past literature to perform very well when checked in closed-loop with well known computer simulators of diabetic patients approved by the Food and Drug Administration as a substitute of animal trials.