<i>H</i><SUB align="right">∞ controller synthesis for multiple time-varying delays systems with application to double diabetes mellitus

Many physical, biological, chemical, electrical, and industrial systems exhibit time-varying delays in their inner dynamics, caused by aftereffects or dead-time phenomena. As the expectation is that the mathematical models of these systems behave like the real process, the techniques to develop control systems should consider these multiple delays. In this context, this paper aims to synthesise a memory-less controller satisfying H∞ performance. More precisely, the controller gain is selected to guarantee closed-loop stability in the presence of delays, by using a Lyapunov-Krasovskii functional (LKF) and a reciprocally convex approach to upper bound integration functions. The closed-loop stability condition is presented as linear matrix inequalities (LMI), solving the stability to extract the optimal controller gain after minimisation of the H∞ performance. The approach is illustrated numerically for a double diabetes mellitus (DDM) system. It is shown that the proposed controller synthesis is simple and the controller gain is able to drive the blood glucose concentration to the desired level upon periodic glucose intakes.