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, Cas d'un système non linéaire

B. Remarque, Chaque fois que des données continues sont discrétisées, il y a toujours une certaine erreur de discrétisation. L'objectif est de réduire la quantité à un niveau jugé négligeable pour réussir à garder le même comportement du système initial (à temps continu). Pour cela, la période d'échantillonnage doit être bien choisie selon la nature et la dynamique du système, vol.6

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. Résumé,

, Si la plupart des travaux concernent les systèmes linéaires et non linéaires temps continu, peu de résultats ont étaient établis dans le cas temps discret. Les travaux de cette thèse portent sur l'observation et la commande d'une classe de systèmes non linéaires à temps discret. Dans un premier temps, le problème de synthèse d'observateur d'état utilisant une fenêtre de mesures glissante est abordé. Des conditions de stabilité et de robustesse moins restrictives sont déduites. Deux classes de systèmes non linéaires à temps discret sont étudiées : les systèmes de type Lipschitz et les systèmes « one-sided Lipschitz ». Ensuite, une approche duale a été explorée afin de déduire une loi de commande stabilisante basée sur un observateur. Les conditions d'existence d'un observateur et d'un contrôleur stabilisant les systèmes étudiés sont formulées sous forme d, L'analyse et la synthèse des systèmes dynamiques ont connu un développement important au cours des dernières décennies comme l'atteste le nombre considérable des travaux publiés dans ce domaine, et continuent d'être un axe de recherche régulièrement exploré

. Mots-clés, Systèmes « one-sided Lipschitz », Optimisation LMI, Stabilité au sens de Lyapunov, Filtrage H ? , Approche avec fenêtre glissante, Commande baséeobservateur, Commande robuste, Systèmes à temps discret, Systèmes Lipschitz