Geodesic
Controlling solutions to a linear differential equation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2009), pp. 25-33

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Both global attainability and global reducibility problems for a control system equivalent to a linear differential equation are positively solved. Furthermore, the existence of a linear equation having a given Cauchy matrix on a given segment and coinciding with given equations on the left and right of that segment is proved. The results obtained allow one to construct a linear equation with the fundamental solutions system possessing preassigned properties. 
@article{VMUMM_2009_3_a4,
     author = {I. N. Sergeev},
     title = {Controlling solutions to a linear differential equation},
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     pages = {25--33},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_3_a4/}
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I. N. Sergeev. Controlling solutions to a linear differential equation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2009), pp. 25-33. http://geodesic.mathdoc.fr/item/VMUMM_2009_3_a4/