A discrete-time model of nonlinear non-autonomous systems

A discretization method is proposed for continuous-time, non-autonomous, and nonlinear systems. The concept of continualization is used to derive a sufficient condition for a given discrete-time system to be an exact discretization of a continuous-time system. The proposed discretization method is based on an approximate solution to this condition, which is computed using Peano-Baker series. As an example, an inverted pendulum subjected to high-frequency excitation is considered. Simulation results show that the proposed method has good performances even with a relatively large sampling interval.