On linear models for nonlinear systems

  • Authors:

  • P. M. MäKilä;J. R. Partington

  • Affiliations:

  • Automation and Control Institute, Tampere University of Technology, P.O. Box 692, Fin-33101 Tampere, Finland;School of Mathematics, University of Leeds, Leeds LS2 9JT, UK

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2003

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Abstract

Best linear time-invariant (LTI) approximations are analysed for several interesting classes of discrete nonlinear time-invariant systems. These include nonlinear finite impulse response systems and a class of nonsmooth systems called bi-gain systems. The Frechet derivative of a smooth nonlinear system is studied as a potential good LTI model candidate. The Frechet derivative is determined for nonlinear finite memory systems and for a class of Wiener systems. Most of the concrete results are derived in an @?"~ signal setting. Applications to linear controller design, to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed.