Robust closed-loop control of plasma glycemia: A discrete-delay model approach

The paper investigates the problem of tracking a desired plasma glucose evolution by means of intra-venous insulin administration. A model-based approach is followed, according to a recent model of the glucose/insulin regulatory system which consists of a discrete-delay nonlinear differential equation model. A disturbance is added to the insulin kinetics in order to model uncertainties concerning both the insulin delivery rate and the mechanism actuating the insulin pump. A feedback control law which yields input-to-state stability of the closed loop error system with respect to such a disturbance is provided, which depends on the glucose and insulin measurements at the present and at a delayed time. In silico simulations validate the theoretical results.