The oxygen demand in a bioreactor should be lower than the dissolved oxygen content. Biomass concentration is one of the most important factors which affect oxygen demand. Moreover, control of the medium substrate concentration is a result of the substrate inhibition phenomenon. Based on the design ideas of a continuous bioprocess which can regulate the biomass concentration, a mathematical model with the extended Monod growth kinetics and impulsive state feedback control is proposed in this paper. Through an analysis of the dynamic properties and a numerical simulation of the continuous bioprocess with impulsive state feedback control, the conditions are obtained for the existence and stability of the system's positive period-1 solution. It is also pointed out that the positive period-2 solution is nonexistent. The results simplify the choosing of suitable operating conditions for continuous bioprocess. it also presents the complete expression of the positive period-1 solution period, which provides the precise feeding time frame for a regularly continuous bioprocess to achieve an equivalent stable output as that of an impulsive bioprocess in the same production environment. The article also presents and discusses aspects of the bioprocess optimization. (C) 2010 Elsevier B.V. All rights reserved.