Controlling Solutions to a Linear Differential Equation / I.N. Sergeev // Vestn. Mosk. Univ., Matem. Mekhan. 2009. № 3. P. 25-33 [Moscow Univ. Math. Bulletin. Vol. 64, No 3, 2009. P. 113-120]
Both global attainability and global reducibility problems for a controllable 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 from 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.