An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations

For monotone linear differential systems with periodic coefficients, the (first) Floquet eigenvalue measures the growth rate of the system. We define an appropriate arithmetico-geometric time average of the coefficients for which we can prove that the Perron eigenvalue is smaller than the Floquet eigenvalue. We apply this method to Partial Differential Equations, and we use it for an age-structured systems of equations for the cell cycle. This opposition between Floquet and Perron eigenvalues models the loss of circadian rhythms by cancer cells.Comment: 7 pages, in English, with an abridged French versio

Duality and separation theorems in idempotent semimodules

We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert's projective metric. We develop more generally a theory of dual pairs for idempotent semimodules. We obtain as a corollary duality results between the row and column spaces of matrices with entries in idempotent semirings. We illustrate the results by showing polyhedra and half-spaces over the max-plus semiring.Comment: 24 pages, 5 Postscript figures, revised (v2

Design of CMOS UWB Pulse Generators

International audienc

Series which are both max-plus and min-plus rational are unambiguous

Consider partial maps from the free monoid into the field of real numbers with a rational domain. We show that two families of such series are actually the same: the unambiguous rational series on the one hand, and the max-plus and min-plus rational series on the other hand. The decidability of equality was known to hold in both families with different proofs, so the above unifies the picture. We give an effective procedure to build an unambiguous automaton from a max-plus automaton and a min-plus one that recognize the same series

Structure de contrôle hiérarchique pour l'optimisation de l'autoconsommation des micro-réseaux de bâtiments

International audienceRenewable energy sources are increasingly deployed as distributed generators, restructuring the traditional electrical grid toward smart grids. Their intermittent power generation makes difficult the development of a complete carbon-free MicroGrid. Hence, aiming to keep the safe operation of a building MicroGrid (BMG) under stochastic variations in the power imbalance while respecting the requirements imposed by grid regulation to maximise self-consumption, a three-level energy management system was designed. The BMG main grid interaction aspects are assured by the two upper control level throughout a hierarchical model predictive control, whereas the power sharing among all electric vehicles is ensured via a deterministic state machine. The entire hierarchical control structure was tested through simulation in MATLAB under different scenarios. Results prove that the proposed control allows the BMG to keep its self-consumption index within expected boundaries despite environmental disturbances

Le football : une culture mondialisée et territorialisée

Le football est marqué par la géographie. Comme tout sport, il est la délimi­tation d’un espace de jeu normé, standardisé (Gay, 1997). Ce rapport entre­tenu avec l’espace situe nécessairement telle ou telle activité physique dans une logique culturelle spécifique, entre sport et jeu, entre système sportif et système ludo-sportif (Darbon, 2014), entre le football et d’autres jeux « balle au pied ». De par la simplicité de ses règles, y compris donc celles de son cadre d’expression, le football..

Duality between invariant spaces for max-plus linear discrete event systems

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.Comment: 22 pages, 3 figures (6 eps files