Lyapunov functionals for linear neutral delay systems in the Hale's form

Abstract

We construct Lyapunov functionals for linear neutral delay systems in the Hale's form. Our construction is made for no differentiable initial functions, as required for such a class of systems, but not thus considered in the existing works. The functionals depend on a special matrix-valued function which is the natural extension of the Lyapunov matrix for retarded delay systems. The constructed functionals allow deriving a converse result for exponential stability of the systems and exponential estimates for the solutions.