ROBUST H∞ CONTROL VIA LMIS FOR AN ARTIFICIAL PANCREAS SYSTEM WITH ACTUATOR SATURATION IN THE LUR’E STRUCTURE

Abstract

This work presents a robust  control approach via linear matrix inequalities applied to an artificial pancreas system described in the Lur'e framework. The adopted glucose-insulin model is based on the Bergman minimal model, considering parametric uncertainties, actuator saturation, and food disturbances. The nonlinearity associated with insulin pump saturation is treated as a sector-specific static nonlinearity, allowing the system to be represented as the interconnection between an uncertain linear block and a feedback nonlinearity. The controller synthesis is performed using a quadratic Lyapunov function, the Bounded Real Lemma, and the S-procedure, resulting in conditions of absolute stability and robust performance expressed in LMIs. Numerical results show that the proposed controller reduces the glycemic peak, decreases settling time, and satisfies the condition , even at the worst vertex of the uncertainty polytope. It is concluded that the proposed methodology constitutes a promising alternative for the development of robust, safe artificial pancreas systems compatible with real physical constraints.