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Representation of solutions of delayed differential equations with multiple delays and periodic coefficients is established. Consequently, results on stabilizability of weakly delayed closed-loop systems and stability of non-weakly delayed periodic systems are proved. The stabilizability result is an extension of the classical Brunovský theorem for linear periodic systems of ordinary differential equations to a class of delay differential equations with pairwise permutable matrix functions.

Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions