Dynamic analysis of the ethanol fermentation with the impulsive state feedback control

• Ethanol fermentation model with the impulsive state feedback control is proposed.
• Existence and stability of the order-1 or order-2 periodic solution are investigated.
• The complete expression of the order-1 periodic solution is obtained.
• Fermentation process can be effectively controlled by monitoring the impulsive period.

To keep a sustainable and steady output of ethanol, ethanol fermentation in a bio-reactor with impulsive state feedback control is formulated. The sufficient conditions for existences of order-1 periodic solution and order-2 periodic solution are obtained by using the properties of the periodic solution. The results imply that ethanol fermentation tends to an order-1 periodic solution or order-2 periodic solution. At the same time, we also give the complete expression of the period of the positive period-1 solution. Finally, discussions and numerical simulations are given.