Asymptotic expansion of the solution of a matrix differential-difference equation of the general form

We obtain the asymptotic expansion of the solution of an inhomogeneous matrix differential-difference equation that belongs to the retarded or neutral type. The case of unbounded delays is considered. We take into account the influence of roots of the characteristic equation. An integral estimate of the remainder with a semimultiplicative weight is obtained depending on the semimultiplicative moment of the free matrix term in the equation.