Nonlinear system analysis by Volterra and Hermite functional expansions

Abstract

The Volterra series method appeared in systems engineering just after the Second World War and has since been widely used for system modelling. The number of papers using it has grown correspondingly although there are still rather few books on the general theory. The present small book is intended as an initial version of a book treating the subject from a mathematical viewpoint giving importance to clear derivation of results and their mathematical justification. Particular attention is given to the convergence of Volterra series arising from the solution of forced nonlinear differential equations. For Gaussian inputs the book describes, alongside the Volterra theory, also the related Hermite functional expansion which covers general Gaussian inputs as well as white noise. For white noise the Hermite expansion coincides with the Wiener G-functional expansion. The Hermite approach has greater generality than the usual treatment based on Wiener’s theory and using properties of Hermite polynomials has more relation to standard mathematical literature. The Hermite approach also has a certain priority over the Wiener G-functional expansion and is related to that of Itô which also preceded it.

The book originates from an undergraduate course on nonlinear systems given many years ago at Eindhoven Technical High School, now Eindhoven University of Technology. It has been completed in the present form while the writer has been a visitor in the signal processing group of the University of Southampton Institute of Sound and Vibration Research.

More information

Identifiers

Catalogue record

Export record