The last chapter of the first part of the book is dedicated to the retarded type linear time-delay systems with distributed delay. First, quadratic functionals with a prescribed time derivative along the solutions of such a system are introduced and Lyapunov matrices that define the functional are derived. Then, such issues as the existence and uniqueness of Lyapunov matrices are studied. A numerical procedure for the computation of Lyapunov matrices is proposed. It is shown that in some cases the computation of the matrices is reduced to the solution of a boundary value problem for an auxiliary system of linear matrix ordinary differential equations. Complete type quadratic functionals are defined, and various application of the functionals are discussed.