Synchronization of LienardType Oscillators in Uniform Electrical Networks
Abstract
This paper presents a condition for global asymptotic synchronization of Lienardtype nonlinear oscillators in uniform LTI electrical networks with series RL circuits modeling interconnections. By uniform electrical networks, we mean that the perunitlength 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 RL circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov and passivitybased arguments that strong coupling is required to ensure synchronization.
 Authors:
 Publication Date:
 Research Org.:
 National Renewable Energy Lab. (NREL), Golden, CO (United States)
 Sponsoring Org.:
 NREL Laboratory Directed Research and Development (LDRD)
 OSTI Identifier:
 1320376
 Report Number(s):
 NREL/CP5D0065194
 DOE Contract Number:
 AC3608GO28308
 Resource Type:
 Conference
 Resource Relation:
 Conference: Presented at the 2016 American Control Conference (ACC), 68 July 2016, Boston, Massachusetts
 Country of Publication:
 United States
 Language:
 English
 Subject:
 24 POWER TRANSMISSION AND DISTRIBUTION; oscillators; synchronization; integrated circuit interconnections; integrated circuit modeling; Lyapunov methods; limitcycles; mathematical model
Citation Formats
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., and Dhople, Sairaj V. Synchronization of LienardType Oscillators in Uniform Electrical Networks. United States: N. p., 2016.
Web. doi:10.1109/ACC.2016.7525600.
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., & Dhople, Sairaj V. Synchronization of LienardType Oscillators in Uniform Electrical Networks. United States. doi:10.1109/ACC.2016.7525600.
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., and Dhople, Sairaj V. 2016.
"Synchronization of LienardType Oscillators in Uniform Electrical Networks". United States.
doi:10.1109/ACC.2016.7525600.
@article{osti_1320376,
title = {Synchronization of LienardType Oscillators in Uniform Electrical Networks},
author = {Sinha, Mohit and Dorfler, Florian and Johnson, Brian B. and Dhople, Sairaj V.},
abstractNote = {This paper presents a condition for global asymptotic synchronization of Lienardtype nonlinear oscillators in uniform LTI electrical networks with series RL circuits modeling interconnections. By uniform electrical networks, we mean that the perunitlength 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 RL circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov and passivitybased arguments that strong coupling is required to ensure synchronization.},
doi = {10.1109/ACC.2016.7525600},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 8
}

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