Discretization of Nonautonomous Nonlinear Systems Based on Continualization of an Exact Discrete Time Model

Abstract

An innovative approach is proposed for generating discretetime models of a class of continuoustime, nonautonomous, and nonlinear systems. By continualizing a given discretetime system, sufficient conditions are presented for it to be an exact model of a continuoustime system for any sampling periods. This condition can be solved exactly for linear and certain nonlinear systems, in which case exact discretetime models can be found. A new model is proposed by approximately solving this condition, which can always be found as long as a Jacobian matrix of the nonlinear system exists. As an example of the proposed method, a van der Pol oscillator driven by a forcing sinusoidal function is discretized and simulated under various conditions, which show that the proposed model tends to retain such key features as limit cycles and spacefilling oscillations even for large sampling periods, and outperforms the forward difference model, which is a wellknown, widelyused, and online computable model.