Observer-based closed-loop control for the glucose-insulin system: local Input-to-State Stability with respect to unknown meal disturbances

Closed-loop glucose control schemes, usually based on intravenous/subcutaneous insulin administration, need to cope with the problem of exogenous glucose intake (e.g. a meal), a disturbance hard to anticipate in timing, in amount and in the rate of effective absorption of the nutrient. In this note, an intravenous feedback control law is considered, based on the use of a Delay Differential Equation (DDE) model of the glucose-insulin system, with the external meal treated as a completely unknown disturbance. It is shown that the closed-loop system satisfies the local Input-to-State Stability (ISS) property with respect to the unknown disturbance. The equivalence between asymptotic stability and local input-to-state stability for retarded nonlinear systems is proven. Simulations show the efficacy of the control algorithm with respect to a standard plasma glucose appearance rate profile following a meal, taken from the literature.