Geodesic
On necessary and sufficient conditions for the controllability of nonlinear systems in small
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 25 (2002) no. 2, pp. 65-66.

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We obtained the necessary and sufficient conditions of local controllability over the nonlinear system. These results are also applied in the «critical» case when the system of linear approximation of the nonlinear system don't locally controllable. 
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Yu. V. Masterkov. On necessary and sufficient conditions for the controllability of nonlinear systems in small. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 25 (2002) no. 2, pp. 65-66. http://geodesic.mathdoc.fr/item/IIMI_2002_25_2_a16/

[1] Tonkov E. L., “Upravlyaemost nelineinoi sistemy po lineinomu priblizheniyu”, Prikladnaya matematika i mekhanika, 38:4 (1974), 599–606 | MR | Zbl

[2] Masterkov Yu. V., “Nekotorye voprosy upravlyaemosti nelineinykh sistem”, Izvestiya Instituta matematika i informatiki UdGU, 1999, no. 2(17), 41–101 | MR