Damping problem for control system with delay with different number of inputs and outputs

We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coefficients and several delays. A connection has been established between the variational problem corresponding to the problem of calming a system with delay and the boundary value problem for a system of second-order differential equations. A priori estimates of solutions are obtained. A theorem on the solvability of the considered boundary value problem is proved.