Solvability of a periodic boundary-value problem for systems of functional differential equations with cyclic matrices

We consider first-order systems of linear functional differential equations with regular operators. For families of systems of two equations we obtain the general necessary and sufficient conditions for the unique solvability of a periodic boundary-value problem. For families of systems of n linear functional differential equations with cyclic matrices we obtain effective necessary and sufficient conditions for the unique solvability of a periodic boundary-value problem.