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                <term xml:lang="en">fasting periods</term>
                <term xml:lang="en">type 1 diabetes</term>
                <term xml:lang="en">positive feedback</term>
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              <p>Positive invariant sets of a biological mathematical model of type-1 diabetes are characterized in this paper. Glycemia is physically a non-negative variable but the presented mathematical model does not guarantee positive trajectories of this state variable for t &gt; 0.Therefore, to give a better mathematical representation of the blood glucose-insulin interaction, invariance conditions of the positivity of the open-loop free-system response are firstly found.Secondly, closed-loop positive invariance is investigated for the ultimate goal of regulating glycemia within normal levels using automated exogenous insulin infusions. The conditions for a standard state feedback control that guarantees a positiveness and stability of the input/state solutions are presented. The resulting non-negative control is virtually tested on diabetic patients to illustrate the theoretical results.</p>
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