Linear feedback-based control of blood glucose in a modified model for glucose–insulin kinetics: A theoretical study

Abstract

In this paper, we present a modified minimal model for glucose and insulin kinetics model. The model proposed here is a smooth approximation of the original non-smooth minimal model. The dynamical properties like dissipativity, existence of equilibrium and stability of the system at the equilibrium points are investigated. A linear feedback-based control strategy is studied to control the blood glucose level in the situation where the physical system fails to regulate the blood glucose level automatically. A critical control parameter value [Formula: see text] is determined in terms of the system parameters. Extensive numerical simulation is performed with different parameter sets. Assuming different values for the feedback gain parameter, ranges of physiological parameter [Formula: see text] are determined where the feedback gain is sufficient to stabilize the control system.