Decomposition of generalized frequency response functions for nonlinear systems using symbolic computation

Abstract

A symbolic manipulation procedure, which both computes and automatically decomposes the generalized frequency response functions of nonlinear rational, polynomial and integrodifferential equation models into a set of closed-form nth order transfer functions, is presented. The symbolic representation exposes the explicit relationship between the model parameters and the nonlinear transfer functions in the frequency domain and leads to important insights into the characterization of nonlinear systems. Examples for each model type are included to demonstrate the symbolic transfer function approach.