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.