Comparative study of Matrix exponential and Taylor series discretization methods for nonlinear ODEs

The discretization of nonlinear systems with input time-delay has always been considered of relevant interest in control system studies. For this reason, two different, new discretization schemes are introduced, based on the Matrix exponential and Taylor series, respectively. They are analyzed for the purpose of identifying their advantages and differences. Numerous comparative simulation studies are performed for two systems, i.e., a simple first order process system and a second order system. Various sampling rates, time-delays, and input signals are inspected. Some valuable concluding remarks are made, in order to facilitate the choice between these two methods for a specific system.