Synchronization of Lienard-Type Oscillators in Uniform Electrical Networks

Brian Johnson, Mohit Sinha, Florian Dorfler, Sairaj Dhople

Research output: Contribution to conferencePaper

27 Scopus Citations


This paper presents a condition for global asymptotic synchronization of Lienard-type nonlinear oscillators in uniform LTI electrical networks with series R-L circuits modeling interconnections. By uniform electrical networks, we mean that the per-unit-length impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation of a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series R-L circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov- and passivity-based arguments that strong coupling is required to ensure synchronization.
Original languageAmerican English
Number of pages6
StatePublished - 2016
Event2016 American Control Conference (ACC) - Boston, Massachusetts
Duration: 6 Jul 20168 Jul 2016


Conference2016 American Control Conference (ACC)
CityBoston, Massachusetts

NREL Publication Number

  • NREL/CP-5D00-65194


  • integrated circuit interconnections
  • integrated circuit modeling
  • limit-cycles
  • Lyapunov methods
  • mathematical model
  • oscillators
  • synchronization


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