Nonlinear influence in the frequency domain: Alternating series

Xingjian Jing, Zi Qiang Lang, Stephen A. Billings

Research output: Journal article publicationJournal articleAcademic researchpeer-review

42 Citations (Scopus)


The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities. The magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series. Sufficient (and necessary) conditions in which the output spectrum can be cast into an alternating series are studied. These results reveal a novel frequency-domain insight into the nonlinear influence on a system, and provide a new method for the analysis and design of nonlinear systems in the frequency domain. Examples are given to illustrate the results.
Original languageEnglish
Pages (from-to)295-309
Number of pages15
JournalSystems and Control Letters
Issue number5
Publication statusPublished - 1 May 2011


  • Alternating series
  • Nonlinear systems
  • Output spectrum
  • Volterra series

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Computer Science(all)
  • Mechanical Engineering

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