Finding the parameters of exponential estimates of solutions to the Cauchy problem for some systems of linear delay differential equations

We consider the problem of constructing component-wise exponentially decreasing estimates of the solution to the Cauchy problem for systems of linear delay differential equations. Systems of differential equations contain matrices of a special type and belong to the systems of Wazewski type equations. The properties of nonsingular M-matrices, methods and algorithms for finding the roots of nonlinear equations are used. Examples of the study of specific systems of differential equations are presented.