Robustness issues of the best linear approximation of a nonlinear system

Johan Schoukens, John Lataire, Rik Pintelon, Gerd Vandersteen, Tadeusz Dobrowiecki

Research output: Contribution to journalArticle

73 Citations (Scopus)


In many engineering applications, linear models are preferred, even if it is known that the system is disturbed by nonlinear distortions. A large class of nonlinear systems, which are excited with a "Gaussian" random excitation, can be represented as a linear system GBLA plus a nonlinear noise source YS. The nonlinear noise source represents that part of the output that is not captured by the linear approximation. In this paper, it is shown that the best linear approximation GBLA and the power spectrum SYS of the nonlinear noise source YS are invariants for a wide class of excitations with a user-specified power spectrum. This shows that the alternative "linear representation" of a nonlinear system is robust, making its use in the daily engineering practice very attractive. This result also opens perspectives to a new generation of dynamic system analyzers that also provide information on the nonlinear behavior of the tested system without increasing the measurement time.

Original languageEnglish
Pages (from-to)1737-1745
Number of pages9
JournalIEEE Transactions on Instrumentation and Measurement
Issue number5
Publication statusPublished - Feb 10 2009


  • Approximation
  • Best linear approximation
  • Excitation
  • Nonlinear distortion
  • Nonlinear system

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering

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