no. 15-16
Automation (theoretical)
Growth bound of delay-differential algebraic equations
[Taux de croissance des équations algébro-différentielles à retards]

Présenté par : Olivier Pironneau

Boisgérault, Sébastien1
1 Mines-ParisTech, CAOR – Centre de robotique, mathématiques et systèmes, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 15-16, pp. 645-648.

Cet article traite des équations algébro-différentielles à retards, un large sous-ensemble des équations différentielles fonctionnelles linéaires à mémoire finie. Nous introduisons différentes représentations des opérateurs de retard, qui fournissent une définition simple du concept de solution de tels systèmes. Ensuite, nous étudions les solutions exponentielles et prouvons que les zéros les plus à droite de la fonction caractéristique dʼun système déterminent son taux de croissance.

This paper deals with delay-differential algebraic equations, a large class of linear and finite-memory functional differential equations. We introduce several representations of delay operators that provide a simple definition for the concept of solutions of such systems. Then we study exponential solutions and prove that the rightmost zeros of a system characteristic function determine its growth bound.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.08.001
Boisgérault, Sébastien 1

1 Mines-ParisTech, CAOR – Centre de robotique, mathématiques et systèmes, 60, boulevard Saint-Michel, 75272 Paris cedex 06, France 
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Boisgérault, Sébastien. Growth bound of delay-differential algebraic equations. Comptes Rendus. Mathématique, Tome 351 (2013) no. 15-16, pp. 645-648. doi : 10.1016/j.crma.2013.08.001. http://www.numdam.org/articles/10.1016/j.crma.2013.08.001/

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