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Title: Synchronization of Lienard-Type Oscillators in Uniform Electrical Networks

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.
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Resource Relation:
Conference: Presented at the 2016 American Control Conference (ACC), 6-8 July 2016, Boston, Massachusetts
Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE)
Research Org:
NREL (National Renewable Energy Laboratory (NREL), Golden, CO (United States))
Sponsoring Org:
NREL Laboratory Directed Research and Development (LDRD)
Country of Publication:
United States
24 POWER TRANSMISSION AND DISTRIBUTION oscillators; synchronization; integrated circuit interconnections; integrated circuit modeling; Lyapunov methods; limit-cycles; mathematical model