Generalized mapping models for the discretization of nonlinear systems

Since exact integration of nonlinear systems is in general impossible, accurate discrete-time models of nonlinear systems have to be derived for control as well as for digital and/or hybrid simulation purposes. This paper proposes generalized mapping model techniques for the discretization of nonlinear systems. In particular, the paper provides: 1) an interpretation and a generalization of mapping models in terms of various hold devices with each one being applied to a different part of the nonlinear system governed by ODEs, and 2) an investigation of the use of scaling functions to decrease the adverse effects of stiff systems with mapping models. Examples demonstrate that mapping models can improve both the accuracy and stability in the modeling and simulation of nonlinear systems.