Further results on robust output feedback control for the chemostat dynamics

We study feedback stabilization problems for chemostats with two species and one limiting substrate, which play an important role in systems biology and population dynamics. We provide a survey of the literature on feedback stabilization for chemostats, and then we construct new dilution rate output feedbacks that stabilize a componentwise positive equilibrium, and only depend on the sum of the species levels. We prove that the feedbacks are robust to model uncertainty. The novelty and importance of our new contribution is in our dropping the usual assumption on the relative sizes of the growth yield constants, and our allowing uncertain uptake functions that are not necessarily concave.