Etude de la structure topologique de l'ensemble des systèmes affines contrôlables en basse dimension

Abstract : From a topological point of vien this work deals with the structure of a set of affine and controllable systems. From the work of (J.S.), (A.S.V.) it appeared that definite relations exist between topological structure of a set of affine controllable systems Ca and Ch. In particuler the properties of Fr Ca and the connexivy of Ca arise direcly from analogouds properties of Ch. We show that Ca gives rise to two types of boundary points. We can expect to have three types of boundary points. The interior of the closed set Ca contains affine controllable systems for which the trajectories are cycles. For the other cases they are on the exterior boundaries, we also show that the interior of Ca is uniquely composed of (J.S.) and affine controllable systems to which correspond homogeneous non-controllable systems characterized by collinear fields (non-independent spirals). Our result is that the set of affine controllable systems Ca is connected
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Abdelouahab Kadem. Etude de la structure topologique de l'ensemble des systèmes affines contrôlables en basse dimension. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1988. Français. ⟨NNT : 1988METZ004S⟩. ⟨tel-01775747⟩

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