A numerical procedure for the construction of Lyapunov matrices is proposed. It is shown that the matrices satisfy an auxiliary two-point boundary value problem for a special delay free system of matrix equations. Some applications of the functionals are also given. In this paper we study the problem of computation of Lyapunov functionals with a prescribed time derivative for the case of delay systems with periodic coefficients. Similar to the case of time invariant systems the functionals are defined by special Lyapunov matrices.