Robust global nonlinear sampled-data regulator for the glucose-insulin system

In this paper we deal with the problem of tracking a desired plasma glucose evolution by means of intra-venous insulin administration, for Type 2 diabetic patients exhibiting basal hyperglycemia. A nonlinear time-delay model is used to describe the glucose-insulin regulatory system, and a modelbased approach is exploited in order to design a global sampleddata control law for such system. Sontag's universal formula is designed to obtain a steepest descent feedback induced by a suitable control Lyapunov-Krasovskii functional. Such a feedback is a stabilizer in the sample-and-hold sense. Furthermore, the input-to-state stability redesign method is used in order to attenuate the effects of bounded actuation disturbances and observation errors, which can appear for uncertainties in the instruments. The proposed control law depends on sampled glucose and insulin measurements. Theoretical results are validated through simulations.