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This article studies the problem of stabilizing a two‐stage continuous bioreactor system. A simple dynamic model of the system is first introduced based on a detailed mass balance model, and then used to derive a constant‐yield controller to stabilize the system at given design steady state conditions. Using Lyapunov stability analysis, this control law is proved to guarantee stability of the closed loop system over the entire positive orthant. Simulation results show the successful performance of the controller. The control law is proved to be robust with respect to errors in the kinetic parameters and in the inlet feed concentration, in the sense of preserving its stability region. Performance of the control system can be enhanced if a feed‐forward measurement of the inlet feed concentration can be incorporated in the control law. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1295–1304, 2018 [ABSTRACT FROM AUTHOR]