A Backstepping Approach for Blood Glucose Control of Parker System

This paper proposes a novel backstepping approach to design a controller for the glucose-insulin model of type I diabetes modeled by the 19th-order Parker system. For this purpose, the system is divided into four parts including two nonlinear dynamic subsystems, a nonlinear static subsystem and a linear one. Based on Lyapunov stability and ISS theorems, the virtual control inputs are designed for each part. The stabilizing virtual inputs are derived based on linear matrix inequality theory which is directly applied to the linear subsystem and indirectly applied to the nonlinear subsystem, based on the Lipschitz condition. Simulation results verify the merits of the proposed approach in handling the effect of external meal disturbance and the blood glucose concentration convergence to its reference value.