H_∞ controller and observer synthesis with delay and nonlinear perturbation of double diabetes systems

Patient having type 1 diabetes mellitus (having insulin resistance experience) cannot be treated solely by treatment procedure of type 1 patient nor does treatment employed for type 2 diabetes work for such patient. This type of diabetes patient needs a specific insulin injection procedure. For continuous insulin injection, the patient has to be classified as a different group from type 1 and type 2 patient. The patients experiencing both type 1 and 2 are called double diabetes mellitus (DDM) patient. Dynamic behavior of the patient was presented in delay differential equation (DDE). Based on the developed DDE of DDM model, controllers and observers fulfilling H_∞ norm bound are designed for this specific group of diabetes mellitus patient. Also, a nominal controller and a nominal observer are synthesized to check the proposed controller's ability for disturbance rejection, which is the glucose intake. The performance of the designed controller and observer is evaluated for a population of simulated patients. It shows that controller and observer are able to regulate and estimate, respectively, glycaemic for population of double diabetes patients.