Markov jump modelling and control of stress effects on the blood glucose regulation system

Diabetes mellitus is a group of metabolic diseases in which there is a malfunction in blood glucose regulatory system. Stress is a random process and has an important role in raising blood sugar level. In this paper, we modify the Bergman´s minimal model to include stress effects as a random process and rewrite the equations to include model uncertainty as well as unknown nonlinear function. Based on a singular system approach, the problems of stochastic stability and robust sliding mode control for blood glucose regulation as a Markov jump system are considered. Therefore control and regulation of glucose-insulin system with respect to stress effects are possible, i.e. blood´s plasma glucose and insulin levels reach their basal values. Finally, the simulation result is given to show the potentials of the proposed method.