Controlling solutions to a linear differential equation / I. N. Sergeev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. ? 3. P. 25-33 [Moscow Univ. Math. Bulletin. Vol. 64, N 3, 2009. P. 113-120].

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.

Key words: linear differential equation, fundamental solutions system, control system, global attainability, global reducibility.