Persistence in ratio-dependent models of consumer-resource dynamics (2007)
Claude Lobry, Frederic Mazenc, Alain Rapaport
In a recent work Cantrell, Cosner and Ruan show that intraspecific interference is responsible for coexistence of many consumers for one resource with a logistic like growth rate. Recently, we have...
Effect on persistence of intra-specific competition in competition models (2007)
An ecological model describing the competition for a single substrate of an arbitrary number of species is considered. The mortality rates of the species are not supposed to have all the same value...
On the Stability of Periodic Solutions in the Perturbed Chemostat (2006)
Mazenc, Frederic, Malisoff, Michael, De Leenheer, Patrick
We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a...
Further Results on Lyapunov Functions for Slowly Time-Varying Systems (2006)
Mazenc, Frederic, Malisoff, Michael
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding...
Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems (2006)
Malisoff, Michael, Mazenc, Frederic
We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions...
Further Results on Active Magnetic Bearing Control with Input Saturation (2006)
Mazenc, Frederic, De Queiroz, Marcio S., Malisoff, Michael, Gao, Feng
We study the low-bias stabilization of active magnetic bearings (AMBs) subject to voltage saturation based on a recently proposed model for the AMB switching mode of operation. Using a...
Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems (2006)
Mazenc, Frederic, Malisoff, Michael, De Queiroz, Marcio S.
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily...
Mazenc, Frederic, Malisoff, Michael
For a broad class of nonlinear systems, we construct smooth control-Lyapunov functions whose derivatives along the trajectories of the systems can be made negative definite by smooth control laws...
Further Remarks on Strict Input-to-State Stable Lyapunov Functions for Time-Varying Systems (2004)
Malisoff, Michael, Mazenc, Frederic
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild...
Global asymptotic stabilization for chains of integrators with a delay in the input (2003)
Frederic Mazenc, Sabine Mondi, Silviu-iulian Niculescu
Abstract. The problem of the global uniform asymp-totic stabilization by bounded feedback of a chain of integrators with a delay in the input is solved. No lim-itation on the size of the delay is...