In this study, three control strategies based on Chebyshev spectral collocation and the Lyapunov-Floquet transformation (LFT) are explored for regulation control of linear periodic time delayed systems. In previous studies, control design based on Chebyhev spectral continuous time approximation (CSCTA) has been demonstrated for the delayed systems and the LFT has been utilized for the control of time-periodic non-delayed systems. However, the combined use of CSCTA and reduced LFT (RLFT) has thus far not been investigated for their application in control design for delayed periodic systems. The delayed Mathieu equation is used as an illustrative example, and the closed-loop response of the system and the control effort are investigated for all three control strategies.

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