Networks of passive oscillators

Vishwesh V. Kulkarni, Marc Riedel, Guy Bart Stan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present new results on the synthesis of globally stable limit cycles in networks of passive oscillators. These passive oscillators can be represented as a modified multi-input-multi-output (MIMO) Lure' system that is dissipative with respect to a certain supply rate. We use KS multipliers to establish the conditions under which the system undergoes either Hopf bifurcation or a pitchfork bifurcation. Under these conditions the network exhibits oscillations. Our results are applicable to networks of non-identical oscillators so long as the each oscillator is a passive oscillator.

Original languageEnglish (US)
Title of host publication2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Pages559-565
Number of pages7
DOIs
StatePublished - Dec 1 2011
Event2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 - Monticello, IL, United States
Duration: Sep 28 2011Sep 30 2011

Publication series

Name2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Other

Other2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
CountryUnited States
CityMonticello, IL
Period9/28/119/30/11

Keywords

  • Hopf bifurcation
  • KS multipliers
  • Lure' systems
  • Zames-Falb multipliers
  • global stability
  • oscillators
  • pitchfork bifurcation

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