Exact Discrete-Time Models for Some Second-Order Nonlinear Systems

For a class of second-order nonlinear systems, this paper presents the exact discretization method based on the linearization of such nonlinear systems using suitable variable transformations. Unlike the existing method that is based on numerical integrations, such as the forward difference model, the derived discrete-time equation gives the values that match exactly those of the differential equation at the discrete-time instants for any discretization interval. Simulation results are presented to confirm the validity of this model