This paper presents optimal control studies of delayed dynamical systems with the help of a method of continuous time approximation (CTA). The CTA method proposes a continuous time approximation of the delayed portion of the response leading to a high and finite dimensional state space formulation of the time-delayed system. Optimal controls of the system such as LQR and output feedback controls are readily designed with the existing design tools. In the paper, we present an output feedback control by means of the mapping approach studied previously. In order to accomplish the objective of control design, we also examine various discretization schemes of the CTA method in frequency domain.

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