Title: H_∞ controller synthesis for multiple time-varying delays systems with application to double diabetes mellitus

Authors: S. Syafiie; F. Tadeo

Addresses: Department of Chemical and Materials Engineering, Faculty of Engineering-Rabigh, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia ' Departamento de ingeneria de sistemas y automatica, Universidad de Valladolid, Valladolid, Spain

Abstract: 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.

Keywords: time-delay systems; multiple delays; H_∞ control; glycaemic regulation; double diabetes mellitus.

DOI: 10.1504/IJESMS.2025.148277

International Journal of Engineering Systems Modelling and Simulation, 2025 Vol.16 No.5, pp.270 - 280

Received: 16 Nov 2023
Accepted: 10 Apr 2024
Published online: 01 Sep 2025 *

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