Geodesic
On Stability of Totally Controlled Systems
Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 94-110

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It is known that a smooth control system whose phase space is a smooth manifold $M$ generates some smooth foliation with singularities. This foliation has the property that, for every point $\eta\in M$, the controllability set with goal point $\eta$ is a subset of the leaf passing through $\eta$. In the first part of the article, we obtain sufficient conditions under which a system totally controlled on a fixed leaf is totally controlled on the leaves close to this leaf. In the second part, we consider a control system with a parameter totally controlled for some value of the parameter. We obtain sufficient conditions under which the system is totally controlled for the values of the parameter close to a given value. 
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     author = {A. Ya. Narmanov},
     title = {On {Stability} of {Totally} {Controlled} {Systems}},
     journal = {Matemati\v{c}eskie trudy},
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     publisher = {mathdoc},
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     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2001_4_1_a5/}
}
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A. Ya. Narmanov. On Stability of Totally Controlled Systems. Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 94-110. http://geodesic.mathdoc.fr/item/MT_2001_4_1_a5/