DC-dominant property of cone-preserving transfer functions

Takashi Tanaka, Cedric Langbort, Valeri Ugrinovskii

Research output: Contribution to journalArticlepeer-review


We consider a class of square MIMO transfer functions that map a proper cone in the space of L2 input signals to the same cone in the space of output signals. Transfer functions in this class have the "DC-dominant" property: the maximum radius of the operator spectrum is attained by a DC input signal and, hence, the dynamic stability of the feedback interconnection of such transfer functions is guaranteed solely by static gain analysis. Using this property, we prove that cone-preserving linear delay differential equations are robustly stable against arbitrary constant delay values. This provides an alternative proof of the delay-independent mean-square stability of a multi-dimensional geometric Brownian motion.

Original languageEnglish (US)
Pages (from-to)699-707
Number of pages9
JournalSystems and Control Letters
Issue number8
StatePublished - Jun 28 2013


  • Delay-independent stability
  • Geometric Brownian motion
  • Mean square stability
  • Monotone dynamical systems
  • Positive systems
  • Small gain theorem

ASJC Scopus subject areas

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

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