Magnitude Bound Characteristics of Nonlinear Frequency Response Functions

  • Xingjian Jing
  • Ziqiang Lang
Part of the Understanding Complex Systems book series (UCS)


In many cases, the magnitude of a frequency response function such as GFRFs can reveal important information about the system, and consequently takes a great role in the analysis of the convergence or stability of the system and the truncation error of the corresponding Volterra series. It can be used to evaluate the significant orders of nonlinearities or the significant nonlinear terms for the magnitude bound, indicate the stability of a system and provide a basis for analysis of system output frequency response. New bound characteristics of both the generalized frequency response functions (GFRFs) and output frequency response for the NARX model are presented in this chapter. It is shown that the magnitudes of the GFRFs and the system output spectrum can all be bounded by a polynomial function of the magnitude bound of the first order GFRF, and the coefficients of the polynomial are functions of the NARX model parameters. These new bound characteristics of the NARX model provide an important insight into the relationship between the model parameters and the magnitudes of the system frequency response functions, reveal the effect of the model parameters on the stability of the NARX model to a certain extent, and provide a useful technique for the magnitude based analysis of nonlinear systems in the frequency domain.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Xingjian Jing
    • 1
  • Ziqiang Lang
    • 2
  1. 1.The Hong Kong Polytechnic UniversityHong KongPR China
  2. 2.The University of SheffieldSheffieldUK

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