This paper presents a novel control strategy for fully automated insulin delivery (fAID) systems aiming to treat people with type 1 diabetes, considering parametric uncertainties in the glucose-insulin model, the sensor noise and delay, and saturation of the control action related to the inability to increase glucose from insulin infusion. A constrained robust regulator for linear discrete-time Markov jump linear systems, incorporating a robust Kalman filter, referred to as a Markovian controller, was designed and validated in-silico as a fAID system. A demanding scenario considering 31 h of duration, 10 adult virtual subjects accepted by the FDA as substitutes for preclinical trials, and four daily meals totaling 200 g of carbohydrates, was used to compute several glycemic indicators in tests with and without sensor signal noise and delay. To assess the robustness of the Markovian controller, 1000 tests were performed, introducing stochastic variations to the scenario, particularly in relation to meals. The Markovian controller obtained high performance, safety, and robustness even in the presence of noise and delay in the glucose signal and without meal announcements. On average, 71.8% of time in range of normoglycemia was obtained for all patients in the 1000 tests. On the other hand, hypoglycemia occurred 0.1% of the time. The Markovian controller effectively regulates glucose without needing meal announcements and demonstrates rapid and effective prevention of postprandial hyperglycemic peaks while avoiding hypoglycemia. This control approach shows great potential to advance further research as a fAID system.