  We characterise the bolus insulin input which minimises the maximum plasma
glucose concentration predicted by the Magdelaine and Bergman minimal models in
response to any positive bounded disturbance whilst remaining above a fixed
lower plasma glucose concentration. This characterisation is in terms of the
maxima and minima of the plasma glucose concentration and limits the
controllability of such systems. Any further attempt to lower the maximum
plasma glucose concentration will result in hypoglycaemia.
