Stabilization in a Chemostat with Sampled and Delayed Measurements and Uncertain Growth Functions

Frédéric Mazenc (1) , Jérôme Harmand (2) , Michael Malisoff (3)

1 DISCO - Dynamical Interconnected Systems in COmplex Environments
2 LBE - Laboratoire de Biotechnologie de l'Environnement [Narbonne]
3 LSU Mathematics - Department of Mathematics [Baton Rouge]

We provide a new control design for chemostats, under constant substrate input concentrations, using piecewise constant delayed measurements of the substrate concentration. Our growth functions can be uncertain and are not necessarily monotone. The dilution rate is the control. We use a new Lyapunov approach to derive conditions on the largest sampling interval and on the delay length to ensure asymptotic stabilization properties of a componentwise positive equilibrium point.

Mots clés: sampling; delay; stabilization; performance testing; output feedback

Mots clés: fonction de croissance; méthode d'échantillonnage; concentration en substrat; contrôle de performance; taux de dilution; chemostat

Domaines: Sciences du Vivant [q-bio]

Frédéric Mazenc, Jérôme Harmand, Michael Malisoff. Stabilization in a Chemostat with Sampled and Delayed Measurements and Uncertain Growth Functions. Automatica, 2017, 78, pp.241-249. ⟨10.1016/j.automatica.2016.12.035⟩. ⟨hal-01604883v2⟩