Stability and Robustness Analysis for a Multi-Species Chemostat Model with Uncertainties

Frédéric Mazenc 1 Michael Malisoff 2 Gonzalo Robledo 3
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : 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.
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Communication dans un congrès
IEEE American Control Conference (ACC) 2017, May 2017, Seattle, United States. IEEE, American Control Conference (ACC), 2017, pp.1-5, 〈10.23919/ACC.2017.7963267〉
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Frédéric Mazenc, Michael Malisoff, Gonzalo Robledo. Stability and Robustness Analysis for a Multi-Species Chemostat Model with Uncertainties. IEEE American Control Conference (ACC) 2017, May 2017, Seattle, United States. IEEE, American Control Conference (ACC), 2017, pp.1-5, 〈10.23919/ACC.2017.7963267〉. 〈hal-01660127〉

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