The minimal mathematical models for exercise and its extension is included the major exercise effects on plasma glucose and insulin levels. Model expectations for glucose and insulin dynamics are steady with current literature statistics. The extended model offers innovative disruption test stage for the enlargement of closed-loop glucose control algorithms. Stability analysis as well as qualitative analysis has been made for the model. We treat the controllability and observability of the system for glucose insulin regulatory system during feedback design. Numerical simulation has been carried out to check the effectiveness and actual behavior for the proposed system.