Picture of scraped petri dish

Scrape below the surface of Strathprints...

Explore world class Open Access research by researchers at the University of Strathclyde, a leading technological university.

Explore

Global reconstruction of nonlinear systems from families of linear systems

Leith, D.J. and Leithead, W.E. (2002) Global reconstruction of nonlinear systems from families of linear systems. In: 15th Triennial World Congress of the International Federation of Automatic Control, 2002-07-21 - 2002-07-26.

[img]
Preview
PDF
1002728057_file_pdf.ps.zip_combining.pdf - Submitted Version

Download (119kB) | Preview

Abstract

This note concerns a fundamental issue in the modelling and realisation of nonlinear systems; namely, whether it is possible to uniquely reconstruct a nonlinear system from a suitable collection of transfer functions and, if so, under what conditions. It is established that a family of frozen-parameter linearisations may be associated with a class of nonlinear systems to provide an alternative realisation of such systems. Nevertheless, knowledge of only the inputoutput dynamics (transfer functions) of the frozen-parameter linearisations is insufficient to permit unique reconstruction of a nonlinear system. The difficulty with the transfer function family arises from the degree of freedom available in the choice of state-space realisation of each linearisation. Under mild structural conditions, it is shown that knowledge of a family of augmented transfer functions is sufficient to permit a large class of nonlinear systems to be uniquely reconstructed. Essentially, the augmented family embodies the information necessary to select state-space realisations for the linearisations which are compatible with one another and with the underlying nonlinear system. The results are constructive, with a state-space realisation of the nonlinear system associated with a transfer function family being obtained as the solution to a number of linear equations.