| Summary: | Presently Type 1 diabetes is global issue and challenges for diabetes public for healthy life. Fully automatic artificial pancreas is well solution for diabetic patients to avoid the hyperglycemia/hypoglycemia as it provided the insulin/glucose when needed. A composite model of Glucagon-Glucose Dynamics is treated for type 1 diabetes mellitus to check the linear controllability and observability of the model and the stability analysis by using Lyapunov function. Two cases are discussed in system according to the input. For case I, Insulin as the input only and glucose as an output and in case II insulin and glucagon as an input and glucose as output only. A control system can only be used in the form of closed-loop control to stabilize the system. This may be show vital part in the progress of fully automatic artificial pancreas and stabilize the control loop system for the Glucose Insulin Glucagon pump. Keywords: Controllability, Observability, Diabetes mellitus, Artificial pancreas, Lyapunov function, Stability analysis
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