H∞ Static Output Feedback Control for a Fractional-Order Glucose-Insulin System

This paper presents the H∞ static output feedback control of nonlinear fractional-order glucose-insulin systems. In this paper, it is an attempt to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of system in the presence of meal disturbance. A static output feedback control is considered for the problem. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order a belongs to 0 < α < 1. Finally, numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are as stable as their integer order counterpart in the presence of exogenous glucose infusion or meal disturbance.