Télécharger La thèse :

Titre: Contribution à l’Observabilité des Systèmes Linéaires Perturbés

Domaine: Mathématiques informatique (MI)

Filière: Mathématique

Option: Théorie Mathématique du Contrôle

Auteur: Barigou Ahmed

Soutenu (e) le: 14/12/2010

Sous la direction de: B. MESSIRDI, Professeur, Université d’Oran

Le président du jury : M. TERBECHE, Professeur, Université d’Oran

Examinateur1: M. M. BEKKAR, Professeur, Université d’Oran

Examinateur2: A. TALHAOUI, Maître de Conférences, ENSET-ORAN

Examinateur3: D. BOUAGGADA, Maître de Conférences, Université de Mostaganem


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(.).

Mots clefs: Bounded operator; Linear system; Bochner integrable perturbation; Hilbert space; Banach space; Ideal observability; Kalman observability; Conditioned invariance; Controlled invariance; Operator factorization.

Publications associées à la thèse

Article 2850:

Titre: Applied Mathematical Sciences (ISSN 1312-885X)

Revue: On the lack of ideal observability in Hilbert space

Référence: Applied Mathematical Sciences, Vol. 4, 2010, no. 59, 2931-2941. 2010

Date: 2010