  In this article, the inverse scattering problem (ISP) of recovering the
matrix coefficient of a first order system of ordinary differential equations
on the half-axis from its scattering matrix is considered. In the case of a
triangular structure of the matrix coefficient, this system has a Volterra-type
integral transformation operator at infinity. Such type of transformation
operator allows to determine the scattering matrix on the half-axis via the
matrix Riemann-Hilbert factorization in the case, where contour is real axis,
normalization is canonical and all the partial indices are zero. The ISP on the
half-axis is solved by reducing it to ISP on the whole axis for the considered
system with the coefficients that are extended to the whole axis as zero.
