Smoothness of solutions to the damping problem for nonstationary control system with delay of neutral type on the whole interval

We consider the damping problem for a nonstationary control system described by of differential-difference equations neutral type with smooth matrix coe cients and several delays. This is equivalent to boundary-value second-order differentialdifference equations, which has unique generalized solution. It proved that smoothness this solution can be violated on considered interval preserved only some subintervals. Su cient conditions initial function are obtained ensure over entire interval.