In this paper, the application of the Magnus expansion on periodic time-delayed differential equations is proposed, where an approximation technique of Chebyshev Spectral Continuous Time Approximation (CSCTA) is first used to convert a system of delayed differential equations (DDEs) into a system of ordinary differential equations (ODEs), whose solution are then obtained via the Magnus expansion. The stability and time response of this approach are investigated on two examples and compared with known results in the literature.

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