Stabilization of two-species chemostats with delayed measurements and haldane growth functions

The stabilization of chemostat models with delayed measurements is a challenging problem that is of significant interest in bioengineering and population biology. Here we solve a class of output feedback stabilization problems for chemostat models with one limiting substrate and two species, having Haldane or Monod growth functions. Our stabilizing feedbacks depend only on (i) a given linear combination of the species concentrations, which are measured with an unknown time delay and (ii) a known upper bound for the delay. The delay bound can be arbitrarily large. Our proof is based on the construction of a Lyapunov-Krasovskii functional.