Solution of systems of linear delay differential equations via Laplace transformation

An approach using the Lambert W function for the analytical solution, free and forced, to systems of delay differential equations with a single delay has been developed in [8], [9]. The solution is expressed in the form of an infinite series of modes written in terms of the matrix Lambert W function. In this paper, we utilize the analytical solution to present a solution in the Laplace domain, present validation examples, and emphasize the analogy of the solution method to systems of ordinary differential equations.