We synthesize a feedback for a fully connected network of identical Liénard-type oscillators such that the phase-balanced equilibrium - the mode where the centroid of the coupled oscillators in polar coordinates is at the origin - is asymptotically stable, and the phase-synchronized equilibrium is unstable. Our approach hinges on a coordinate transformation of the oscillator dynamics to polar coordinates, and periodic averaging theory to simplify the examination of multiple time-scale behavior. Using Lyapunov- and linearization-based arguments, we demonstrate that the oscillator dynamics have the same radii and balanced phases in steady state for a large set of initial conditions. Numerical simulation results are presented to validate the analyses.
|Original language||English (US)|
|Title of host publication||2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - Jan 18 2018|
|Event||56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia|
Duration: Dec 12 2017 → Dec 15 2017
|Name||2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017|
|Other||56th IEEE Annual Conference on Decision and Control, CDC 2017|
|Period||12/12/17 → 12/15/17|
Bibliographical noteFunding Information:
M. Sinha and S. V. Dhople were supported in part by the National Science Foundation under the CAREER award, ECCS-CAR-1453921, and grant ECCS-1509277. F. Dörfler was supported by ETH Zürich funds and the SNF Assistant Professor Energy Grant #160573. B. Johnson was supported by the U.S. Department of Energy (DOE) Solar Energy Technologies Office under Contract No. DE-EE0000-1583 and by the DOE under Contract No. DE-AC36-08-GO28308 with NREL.