This paper extends our earlier work on continuous-time approximation of time-delayed dynamical systems by introducing a lowpass filter-based approach. The proposed method substantially improves the accuracy of predictions in frequency as well as time domain. It is applicable to linear and nonlinear dynamical systems, and can be readily incorporated with real-time controls. In the paper, we first review the mathematics literature on numerical methods for delayed differential equations including the equivalent abstract Cauchy problem. We show that the mathematics work provides a solid foundation for several well-studied numerical methods for time-delayed dynamical systems in the engineering literature. Examples are presented to show the accuracy of the pole prediction for linear systems, and temporal responses for linear and nonlinear systems. Furthermore, we discuss the bandwidth issue of the method, and demonstrate that many extraneous poles introduced by the discrete approximation of the time-delayed system that do not match any exact poles of the system are still very important and contribute to the accuracy of temporal responses.
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