Second order hold and taylor series based discretization of SISO input time-delay systems

Second order hold is a method that enables the discretization of input-driven nonlinear systems to be carried out with high precision. A new discretization scheme combining second order hold with the Taylor-series is proposed. The sampled-data representation and mathematical structure are explored. Both exact and approximate sampled-data representations are described in detail. The performance of the proposed algorithm is evaluated for three different systems. Various sampling rates, delay times and truncation orders of the Taylor-series are considered to investigate the proposed method. The results demonstrate that the proposed scheme is practical and easy to use for time-delay systems. Comparisons between the second, first and zero orders are given to show the advantages of the proposed method.