Robust $H_{\infty}$ Control for Type 1 Diabetes Model: A Switching System Approach

This paper is concerned with the problem of H∞ state feedback controller design for the type 1 diabetes switching model. Firstly, the glucose-insulin dynamic system is modeled as a switching system with input constraints and external disturbances. Then, the existence condition of the H∞ state feedback controller is given from the angle of linear matrix inequalities, which makes the resulting closed-loop system to be asymptotically stable and has pre-specified H∞ performance and input constraints. In addition, the H∞ state feedback controller gain can be easily obtained by solving the linear matrix inequalities via the MATLAB toolbox YALMIP. Finally, the proposed approach is applied to a practical example, which explains the validity of theory results.