Summary: In addition to meal intake, a diabetes system has a feedback behavior to balance the constituents of the chemicals, which causes instability. Therefore, a search for a feedback system that can stabilize the system with the introduced disturbances is a concern. In this article, a technique to stabilize a closed-loop system that considers the time-varying delay and rejecting disturbances is introduced. The closed-loop stability technique is designed and analyzed based on a selected suitable Lyapunov-Krasovskii functional (LKF) and satisfying the \(\mathrm{H}_\infty\) performance, and the integral part is upper bounded by a reciprocally convex inequality approach. The optimal closed-loop controller gain is obtained from the feasibility of the linear matrix inequality (LMI) by considering the minimum of the \(\mathrm{H}_\infty\) norm bound. To check the ability and performance of the proposed technique for the stability study, it is numerically applied to govern the blood glucose concentration of a 70kg male patient co-experiencing both types (type 1 and 2) diabetes upon periodically glucose intake as external disturbances. The experiencing of the hybrid diabetes is achieved by varying the beta-cell functioning in insulin production. The proposed technique is able to stabilize and maintain the desired blood glucose concentration being inside a normal healthy range with both glucagon-glycogen conversion and insulin secretion delays.