Robust dynamic output feedback control of blood glucose level in diabetic rat with robust descriptor Kalman filter

•Considering a time-varying uncertain model of Type-1 Diabetic rat.•Proposition of appropriate controller for the singular model of diabetic rat.•Design of μ-synthesis and H∞ controllers, under disturbance and stochastic noise.•Proposing a robust estimator for descriptor model of the diabetic rat.•Connecting the robust controller to the estimator to improve the control action. This paper deals with the robust control problem for a model of blood glucose system in Type-1 diabetic rats with disturbances (food, physical activity, and insulin sensitivity parameter) and model uncertainties. The considered model has a special structure, which can be written as a descriptor model. The robust control law is designed such that the output of the system tracks the desired reference signal despite the parameter uncertainties. By utilizing the μ-synthesis-based and H∞ controller design methods, the desired input signals (insulin for injection) are designed for both approaches and compared with each other. Moreover, the control structure is considered in a way that the states are not essential to be directly measured, and instead, the states estimation is utilized which operates in the closed-loop system together with a control law. Due to the existence of the model uncertainties, external disturbances, and also the characteristics of the descriptor system, the robust descriptor Kalman filter is designed for this system. Finally, to demonstrate the efficiency of the proposed methods, they are applied to the model, and simulations are provided. The results show the closed-loop system including the descriptor model, robust controller, and robust descriptor Kalman filter can force the blood glucose level to maintain in the normal range successfully with an acceptable state estimation error.