Semi-discretization is an effective method for analysis and control design of time-invariant as well as periodic linear systems with time delay. This paper briefly describes various approximation schemes in conjunction to the semi-discretization method. Comparison measures making use of the stability bounds of control gains and the controlled response of the system are presented. The accuracy and efficiency of the method with the zeroth order, improved zeroth order and first order approximations are compared through numerical simulations. Another first order approximation of the system with multiple time delays under a non-delayed feedback leads to integro-differential equations where a simple approximation is utilized to generate discrete maps. It is found that the first order approximation provides substantial improvements in accuracy and efficiency for feedback control design of LTI and periodic systems.

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