Robustness properties preservation in suboptimal T1DM H∞ control: ω‐SPR substitutions

Summary Suboptimal controllers have been proposed to deal with robust glucose regulation problem at type 1 diabetic patients. The features of such controllers involve robust stability and robust performance. These suboptimal controllers are designed at a specific frequencies response, which corresponds to a diabetic type 1 under specific physiological conditions. An open problem stands for preservation of the robustness controller properties for a different frequencies interval beyond the used for designing. This problem is motivated by the possibility of finding distinct frequency response at T1DM patients around the world or under different physiological conditions. In this contribution, the SPR functions are exploited to analyze the robust stability and robust performance preservation. This analysis is done for each one transfer function in closed‐loop related to intake; our results are relevant because of the design range of the controllers can be extended which means that the controllers can be used on the patients with different physiological conditions.