Global dynamics of the chemostat with different removal rates and variable yields (2009)
Sari, Tewfik, Mazenc, Frédéric
In this paper, we consider a competition model between $n$ species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that...
Global dynamics of the chemostat with different removal rates and variable yields (2009)
Sari, Tewfik, Mazenc, Frédéric
In this paper, we consider a competition model between $n$ species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that...
Frédéric Mazenc, Michael Malisoff, Jérôme Harmand
Abstract — We study a two species chemostat model with one limiting substrate. We design feedback controllers so that an equilibrium with arbitrary prescribed species concentrations becomes...
Lyapunov Function Constructions for Slowly Time-Varying Systems (2008)
Frédéric Mazenc, Michael Malisoff
Abstract — We provide general methods for explicitly constructing strict Lyapunov functions for general nonlinear slowly time-varying non-autonomous systems. Our results apply to cases where the...
Polytopic Lyapunov functions for persistence analysis of competing species (2005)
Grognard, Frédéric, Mazenc, Frédéric, Rapaport, Alain
We show that stability of the equilibrium of a family of interconnected scalar systems can be proved by using a sum of monotonic ${\mathcal C}^0$ functions as Lyapunov function. We prove this result...
Polytopic Lyapunov functions for persistence analysis of competing species (2005)
Grognard, Frédéric, Mazenc, Frédéric, Rapaport, Alain
We show that stability of the equilibrium of a family of interconnected scalar systems can be proved by using a sum of monotonic ${\mathcal C}^0$ functions as Lyapunov function. We prove this result...
Polytopic Lyapunov functions for persistence analysis of competing species (2005)
Grognard, Frédéric, Mazenc, Frédéric, Rapaport, Alain
We show that stability of the equilibrium of a family of interconnected scalar systems can be proved by using a sum of monotonic ${\mathcal C}^0$ functions as Lyapunov function. We prove this result...
Lyapunov stability analysis for nonlinear delay systems (2001)
Su cient conditions ensuring that a nonlinear system with disturbances having a delay is delay independent globally asymptotically stable are given. The proof carried out relies extensively on a...
Praly : Strict Lyapunov Functions for Feedforward Systems and Applications (2000)
For nona ne nonlinear feedforward systems classes of control Lyapunov functions are constructed. Explicit formulas are determined in an important particular case. As an application of this design, we...