Static Output Feedback Stabilization of Nonlinear Fractional-Order Glucose-Insulin System

Diabetes is a long-term disease during which the body's production and use of the insulin are impaired, causing glucose concentration level to increase in the bloodstream. The blood glucose dynamics is described using the generalized minimal model structure for the intravenously infused insulin blood glucose, which can represent a wide variety of diabetic patients. In this paper, it is an attempt to incorporate fractional-order derivative into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to determine, mathematically, how the order of a fractional differential system affects the dynamics of system. The paper presents the asymptotical stabilization problem of nonlinear fractional-order glucose insulin systems. A static output feedback control is considered for the problem. Sufficient conditions for the asymptotical stabilization of the nonlinear fractional-order glucose-insulin system are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order \alpha belonging to 0<\alpha<1. Finally, numerical simulations are carried out to illustrate our proposed results. These numerical simulations show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart.