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## Archive of Issues

Uzbekistan Tashkent
Year
2022
Volume
32
Issue
1
Pages
81-93
 Section Mathematics Title The stability of completely controllable systems Author(-s) Narmanov A.Ya.a, Abdishukurova G.M.a Affiliations National University of Uzbekistana Abstract The subject of this paper is the stability of completely controllable systems defined on a smooth manifold. It is known that the controllability sets of symmetric systems generate singular foliations. In the case when the controllability sets have the same dimension, a regular foliation arises. Thus, the possibility of applying the methods of foliation theory to control theory problems arises. This paper presents some of the authors' results on the possibility of applying the theorems on the stability of leaves to the problems on the stability of completely controllable systems and on the geometry of attainability sets. Smoothness throughout the work will mean smoothness of class $C^{\infty}$. Keywords control systems, controllability sets, orbit of vector fields, singular foliation UDC 517.936, 517.925.53 MSC 37C10, 57R27 DOI 10.35634/vm220106 Received 17 December 2021 Language English Citation Narmanov A.Ya., Abdishukurova G.M. The stability of completely controllable systems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 1, pp. 81-93. References Narmanov A.Ya. Controllability sets of control systems that are fibers of a foliation of codimension one, Differentsial'nye Uravneniya, 1983, vol. 19, no. 9, pp. 1627-1630 (in Russian). http://mi.mathnet.ru/eng/de4960 Narmanov A.Ya. A stability theorem for noncompact leaves of a foliation of codimension one, Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya, 1983, no. 19 (4), pp. 100-102. https://zbmath.org/?q=an:0564.57020 Narmanov A.Ya. 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