The process of anaerobic digestion is a common application in the treatment of industrial and communal wastewater treatment plants. The biochemical reactions taking place inside the fermenter can be described by a system of first order differential equations of the biomass and the limiting substrate. Biogas, a byproduct of the anaerobic digestion process is a useful energy source and thus wastewater treatment plants usually aim at maximizing its productivity yield. When the fermenter operates near optimal conditions that maximize biogas production rate though, the process is marginally stable. The intuitive idea of constant-yield control is known to improve the stability properties of the anaerobic digestion process by enlarging the stability region. In the present study, we develop a mathematical formulation of constant-yield control in the presence of biomass decay and endogenous metabolism, with main emphasis on stability analysis. In particular, we derive concrete formulas to estimate the size of the stability region of the closed loop system, and demonstrate the effectiveness of the proposed control strategy in enlarging the stability region. (C) 2013 Elsevier B.V. All rights reserved.