Global reconstruction of nonlinear systems from families of linear systems

D.J. Leith, W.E. Leithead

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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.
Original languageEnglish
Number of pages6
Publication statusPublished - 2002
Event15th Triennial World Congress of the International Federation of Automatic Control - Barcelona, Spain
Duration: 21 Jul 200226 Jul 2002


Conference15th Triennial World Congress of the International Federation of Automatic Control


  • nonlinear systems
  • linear systems
  • linear equations

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