Analytical solution of a system of homogeneous delay differential equations via the Lambert function

A new approach to obtain an analytic solution for delay differential equations (DDE) based on the concept of Lambert functions is presented in this paper. The similarity of the results with the concept of the state transition matrix in ordinary differential equations enables the approach to be used for general classes of linear delay differential equations including the matrix form of DDE. Stability criteria for delay equations in different cases are studied and the results are presented in the paper.