Variation diminishing Hankel operators

Christian Grussler, Rodolphe Sepulchre

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper studies the variation diminishing property of linear time-invariant Hankel k-positive systems, i.e., systems whose Hankel operator maps inputs with k - 1 sign changes to outputs with at most the same variation. Our main result is that these systems have a dominant approximation in the form of a parallel interconnection of k positive lags, that is, first order positive systems. This is shown by expressing the k-positivity of a LTI system as the external positivity (that is, 1-positivity) of k compound LTI systems. Our characterizations are generalizations of the well known properties of positive systems (k = 1) and Hankel totally positive systems (k = 8).

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
Number of pages6
ISBN (Electronic)9781728174471
StatePublished - 14 Dec 2020
Externally publishedYes
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: 14 Dec 202018 Dec 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control


Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island


  • Hankel operator
  • Total positivity
  • external positivity
  • k-positivity
  • positive systems
  • variation diminishing

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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