Thèses de Doctorat "Mathématique"

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Contribution à l’Observabilité des Systèmes Linéaires Perturbés
(Université Oran1 Ahmed Ben Bella, 2010-12-14) Barigou Ahmed
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(.).