Stability and robustness analysis for a multi-species chemostat model with uncertainties

We prove stability and robustness results for chemostat models with one substrate, an arbitrary number of species, a constant dilution rate, and constant inputs of the species. Unlike all previous works, we prove input-to-state stability under uncertainties in important cases where the controls are the input nutrient concentration and the species inputs. Our assumptions ensure global asymptotic stability for an equilibrium, which can allow persistence of multiple species, when the uncertainties are zero. We allow arbitrarily large bounds on the uncertainties in the species dynamics, and equilibria that can be in the boundary of the state space.