Frequency domain analysis for non-linear Volterra systems with a general non-linear output function

Abstract

For non-linear Volterra systems which include a non-linear state equation and a general non-linear output function, the system frequency response functions and some related frequency response characteristics are developed and discussed in this study. These new results establish the frequency response functions for this general form of non-linear systems by extending some existing theory, and provide an analytical insight into the relationship between model parameters and frequency response functions, and the relationship between model parameters and the magnitude bound of frequency response functions. Several examples are given to illustrate the new results.

Acknowledgements

The authors gratefully acknowledge the anonymous referees for their constructive suggestions. The authors also acknowledge the support of the EPSRC-Hutchison Whampoa Dorothy Hodgkin Postgraduate Award, for this work.