The availability of novel technologies for exogenous insulin release and continuous glucose monitoring have increased the possibilities of developing an artificial pancreas. This contribution tackles the design of a H ∞ -based controller to manage glycemia in Type 1 diabetes mellitus (T1DM) under two scenarios: exercise and nocturnal hypoglycemia. Two biosignals are integrated to the blood glucose control problem: lactate is used in exercise scenario, while adrenaline releasing is used for nocturnal hypoglycemia. The effects of each scenario are represented by weighting transfer functions at the control design. Each weighting function accounts the effect of hepatic glucose production and defines separately the following relations: (a) from plasmatic glucose to lactate during exercise and (b) from plasmatic glucose to adrenaline during nocturnal hypoglycemia. Also, the controller is designed by adding a frequency restriction in control signal to incorporate frequency components by the pancreatic insulin release pattern in a healthy subject. A nonlinear physiological model, including Glucose-Insulin-Glucagon dynamics and counter-regulatory effects, is used to show the time-response of the closed-loop including actuator dynamics and parametric changes. levels due to exogenous events (as, among others, different kinds of carbohydrate load during meal, glucose uptake during exercise) or endogenous events (as changes in hepatic or renal glucose production and uptake). From the control theory viewpoint, the exogenous events can be formulated as disturbances while the endogenous ones can be seen as uncertain parameter changes. Thus, the controlled plant corresponding to the diabetic patient is a nonlinear dynamical system with parametric uncertainties and uncertain disturbance inputs. In this sense, although control design is not an easy task, this problem has been addressed mainly via four control approaches with promissory results: model-based predictive control [10], adaptable techniques [11], fuzzy logic [12], and H ∞ robust control [13,14]. As a matter of fact, there are recent promising in silico and in vivo clinical trials of closed-loop glucose control (mainly classic PI and PID schemes [15], as well as advanced techniques such as nonlinear model predictive control [16][17][18][19]) using subcutaneous insulin delivery and subcutaneous continuous glucose monitoring. Such proofs have highlighted promising results using feedback control schemes in glucose control. Although classical PI or PID schemes have used in clinical devices since 70s, it is known that robustness margin of classical controllers can be improved.Respect to H ∞ approaches, the synthesis for blood glucose control is based on the plant frequency response in such manner that the control design ensures closed-loop performance in the frequency interval where plant is sensitive. The controller captures the frequency components and is capable to ensure closed-loop stability in an optimal or suboptimal sense. Moreover, as parametric uncertainties are incl...

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Summary Suboptimal H∞ 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 H∞ 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.

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