Decomposition of Generalised Frequency Response Functions for Non-Linear Systems Using Symbolic Computation

A symbolic manipulation procedure, which both computes and automatically decomposes the generalised frequency response functions of non-linear rational, polynomial and integro-differential equation models into a set of closed-form n-th order transfer functions is presented. The symbolic repression exposes the explicit relatinship between the model parameters and the non-linear transfer functions in the frequency domain and leads to important insights into the characterization of non-linear systems. Examples for each model type are included to demonstrate the symbolic transfer function approach.