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RÉSUMÉ. Dans cet article, à partir d’une relecture de la consistance des systèmes commutés linéaires, la propriété de consistance pour les systèmes non-linéaires de type Lur’e commutés à temps discret est étudiée. Une discussion montre qu’il faut considérer le plus petit majorant quadratique possible de la performance au lieu de la valeur optimale elle-même (qui coïncident dans le cadre linéaire) pour permettre l’extension. Un problème d’optimisation sous contraintes LMI est proposé pour obtenir une stratégie de type min-switching satisfaisant la consistance en non-linéaire. Dans un second temps, cette contribution est utilisée pour la synthèse d’un contrôleur à données échantillonnées avec un échantillonnage non uniforme. Un exemple numérique est alors proposé pour mettre en évidence les apports de ces résultats.
ABSTRACT. In this paper, starting from a rereading of the consistency notion for switched linear systems, the consistency is studied for discrete-time switched Lur’e type systems. A discussion highlights that the smallest upper bound of the cost function should be considered instead of the optimal value (even if they coincide in the linear case) to allow the extension in the nonlinear framework. An optimization problem with LMI constraints is provided to design a minswitching strategy that is consistent in the nonlinear case. Moreover this contribution is used for the synthesis of a sampled data controller with non uniform sampling. A numerical illustration is proposed to show the relevance of these results.
système non linéaire de type Lur’e, commande à données échantillonnées, échantillonnage non uniforme, consistance des systèmes commutés
Ce travail a été partiellement soutenu par le septième programme-cadre de la communauté européenne (FP7/2007-2013) sous la convention de subvention n◦257462: HYCON2 Network of Excellence "Highly-Complex and Networked Control Systems", par le projet ANR COMPACS - "Computation Aware Control Systems", ANR-13-BS03-004, ainsi que par la Région Lorraine.
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