Multiple-time-delay H $$_\infty$$ controller synthesis for glycemic regulation of a hybrid diabetes system

A mathematical model is used to represent a physical system. To mimic closely to a real system, the mathematical model may present in functional differential equations. Most of the processes exhibit multiple time-varying delayed phenomena. This paper aims to develop a memory-less controller that achieves H\(_\infty\) performance for disturbance rejection. The proposed technique for controller design ensures closed-loop stability of a chosen Lyapunov-Krasovskii functional (LKF). while, the integral functions derived from the LKF’s derivative are addressed through the utilization of free matrix inequality The development of stability condition is presented in linear matrix inequality. Based on the developed stability condition, the optimal controller gain is obtained after minimization of the H\(_\infty\) performance. The proposed controller design technique is simulated to stabilize a diabetes system upon periodic glucose absorption as a disturbance function. Clearly, the controller is able to regulate insulin maintaining the blood glucose concentration to the healthy patient concentration upon introducing meal ingestion as periodic disturbances. Compare to an existing method, the proposed controller has lower peak in the rejecting the introducing disturbances.