Sample-data output-feedback parameter variable control of glucose for type 1 diabetes mellitus patients

Abstract

This paper presents a new approach for nonlinear sampled-data output-feedback control of blood glucose concentration (BGC) in patients with type 1 diabetes mellitus (T1DM). The Bergman minimal model (BMM) describing the glucose-insulin regulatory system is framed as a linear parameter-varying (LPV) model that the sampled glucose measurement with the quantized insulin infusion is considered as input delay. The proposed method utilizes the input-delay approach based on a parameter-dependent Lyapunov–Krasovskii functional (LKF) and provides the parameterized matrix inequality conditions for the design of the controller. Using the slack variables, the design conditions are converted to a new form that can achieve feasible solutions by solving a limited number of bilinear matrix inequality. The proposed architecture guarantees stability in a compact set of states for all the trajectories with the parametric uncertainty to address the issue of inter-patient variability. Simulation results confirm that the proposed sampled-data static output-feedback LPV controller with only glucose measurement regulates the BGC despite the parametric uncertainty and meal disturbances in T1DM patients.