Contribution à l’Observabilité des Systèmes Linéaires Perturbés
Contribution à l’Observabilité des Systèmes Linéaires Perturbés
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Date
2010-12-14
Auteurs
Barigou Ahmed
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Éditeur
Université Oran1 Ahmed Ben Bella
Résumé
This thesis is mainly devoted to the ideal observability of abstract linear systems with bounded operators. The contributions brought in this context may be considered as the extensions to Hilbert space of the fundamental results developed up to now in the finite dimensional spaces. The systems considered all along this work will be supposed to be governed in their phase space by the triple (A;B;H) according to the
equations: (1.1) x’(t) = Ax(t) + Bu(t); t=>0;
(1.2) y(t) = Hx(t); t in [0; T] :
Shortly speaking, our aim will be the reconstructibility of the state trajectory x(.) of (1.1) on the observation time interval [0; T] ; for given A; B; and H; and solely from the knowledge of the output y(.) generated
according to (1.2) under the action of the disturbance u(.).
Description
Mots-clés
Bounded operator, Linear system, Bochner integrable perturbation, Hilbert space, Banach space, Ideal observability, Kalman observability, Conditioned invariance, Controlled invariance, Operator factorization