This paper presents a condition for global asymptotic synchronization of Liénard-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 language||English (US)|
|Title of host publication||2016 American Control Conference, ACC 2016|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - Jul 28 2016|
|Event||2016 American Control Conference, ACC 2016 - Boston, United States|
Duration: Jul 6 2016 → Jul 8 2016
|Name||Proceedings of the American Control Conference|
|Other||2016 American Control Conference, ACC 2016|
|Period||7/6/16 → 7/8/16|
Bibliographical noteFunding Information:
Their work was supported in part by the National Science Foundation through award 1509277, and CAREER award 1453921. His work is supported by ETH funds and the SNF Assistant Professor Energy Grant #160573. His work was supported by the Laboratory Directed Research and Development Program at NREL
© 2016 American Automatic Control Council (AACC).