Section: New Results

A Stabilization problem in chemostats

Participants : Frédéric Mazenc [correspondent] , Jérôme Harmand [LBE INRA, EPI MODEMIC] .

We have considered the classical model of the chemostat (which is a bio-reactor) with one substrate, one species and a Haldane type growth rate function is considered. The input substrate concentration is supposed to be constant and the dilution rate is considered as the control. The problem of globally asymptotically stabilizing a positive equilibrium point of this system in the case where the measured concentrations are delayed and piecewise constant with a piecewise constant control is addressed. The result relies on the introduction of a dynamic extension of a new type. [56] .