Synchronization of nonlinear circuits in dynamic electrical networks with general topologies

Sairaj V. Dhople, Brian B. Johnson, Florian Dorfler, Abdullah O. Hamadeh

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain; and ii) a collection of these circuits are coupled through either uniform or homogeneous LTI electrical networks. Uniform electrical networks have identical per-unit-length impedances. Homogeneous electrical networks are characterized by having the same effective impedance between any two terminals with the others open circuited. Synchronization in these networks is guaranteed by ensuring the stability of an equivalent coordinate-transformed differential system that emphasizes signal differences. The applicability of the synchronization conditions to this broad class of networks follows from leveraging recent results on structural and spectral properties of Kron reduction - a model-reduction procedure that isolates the interactions of the nonlinear circuits in the network. The validity of the analytical results is demonstrated with simulations in networks of coupled Chua's circuits.

Original languageEnglish (US)
Article number6883261
Pages (from-to)2677-2690
Number of pages14
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number9
StatePublished - Sep 2014
Externally publishedYes


  • Kron reduction
  • Nonlinear circuits
  • Synchronization


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