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 by Asl And Ulsoy (2003) and Yi and Ulso (2006). 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