Geodesic
High-Order Control Variations and Small-Time Local Controllability
Serdica Journal of Computing, Tome 4 (2010) no. 1, pp. 85-92.

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The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is studied and a new sufficient STLC condition is proved.
Keywords: Local Approximations of the Reachable Set, Smooth Control Systems, Small-Time Local Controllability 
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Krastanov, Mikhail. High-Order Control Variations and Small-Time Local Controllability. Serdica Journal of Computing, Tome 4 (2010) no. 1, pp. 85-92. http://geodesic.mathdoc.fr/item/SJC_2010_4_1_a7/