Abstract
We establish some properties of homogeneous bilinear systems, in particular that controllability is not altered by small perturbation of the coefficients. We obtain sufficient conditions for controllability for nonhomogeneous bilinear systems, with single not uniformly bounded inputs, similar to the results obtained by Jurdjevic and Kupka in the homogeneous case.
Résumé
On établit certaines propriétés des systèmes asservis bilinéaires homogènes; en particulier on montre la stabilité de la contrôlabilité sous l'effet d'une petite perturbation des coefficients du système. On obtient des conditions suffisantes de contrôlabilité pour les systèmes bilinéaires non homogènes à entrée scalaire non uniformément bornée comparables à celles obtenues par Jurdjevic et Kupka dans le cas homogène.
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Bonnard, B. Contrôlabilité des Systèmes Bilinéaires. Math. Systems Theory 15, 79–92 (1981). https://doi.org/10.1007/BF01786974
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DOI: https://doi.org/10.1007/BF01786974