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Linear Approximations of Nonlinear FIR Systems for Separable Input Processes
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2005 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 41, no 3, 459-473 p.Article in journal (Refereed) Published
Abstract [en]

Nonlinear systems can be approximated by linear time-invariant (LTI) models in-many ways. Here, LTI models that are optimal approximations in the mean-square error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is presented. This condition says that the in ut should be separable of a certain order, i.e., that certain conditional expectations should be,P linear. For the special case of Gaussian input signals, this condition is closely related to a generalized version of Bussgang's classic theorem about static nonlinearities. It is shown that this generalized theorem can be used for structure identification and for the identification of generalized Wiener-Hammerstein systems.

Place, publisher, year, edition, pages
Elsevier, 2005. Vol. 41, no 3, 459-473 p.
Keyword [en]
System identification, Mean-square error, Nonlinear systems, Linearization
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-46142DOI: 10.1016/j.automatica.2004.11.016OAI: oai:DiVA.org:liu-46142DiVA: diva2:267038
Note

© 2004 Elsevier Ltd. All rights reserved.

Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Enqvist, MartinLjung, Lennart

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