Version 1
: Received: 22 August 2022 / Approved: 24 August 2022 / Online: 24 August 2022 (13:19:50 CEST)
How to cite:
Kudeyt, M.; Kıvılcım, A.; Köksal Ersöz, E.; Karabacak, Ö. Certification of Almost Global Phase Synchronization of Coupled Oscillators. Preprints2022, 2022080422. https://doi.org/10.20944/preprints202208.0422.v1
Kudeyt, M.; Kıvılcım, A.; Köksal Ersöz, E.; Karabacak, Ö. Certification of Almost Global Phase Synchronization of Coupled Oscillators. Preprints 2022, 2022080422. https://doi.org/10.20944/preprints202208.0422.v1
Kudeyt, M.; Kıvılcım, A.; Köksal Ersöz, E.; Karabacak, Ö. Certification of Almost Global Phase Synchronization of Coupled Oscillators. Preprints2022, 2022080422. https://doi.org/10.20944/preprints202208.0422.v1
APA Style
Kudeyt, M., Kıvılcım, A., Köksal Ersöz, E., & Karabacak, Ö. (2022). Certification of Almost Global Phase Synchronization of Coupled Oscillators. Preprints. https://doi.org/10.20944/preprints202208.0422.v1
Chicago/Turabian Style
Kudeyt, M., Elif Köksal Ersöz and Özkan Karabacak. 2022 "Certification of Almost Global Phase Synchronization of Coupled Oscillators" Preprints. https://doi.org/10.20944/preprints202208.0422.v1
Abstract
Phase synchronization of weakly coupled limit cycle oscillators are related to the stability of the zero solution of the reduced-order dynamics of phase differences, represented by a systems of differential equations on a hypertorus. Using Rantzer's density function, a dual form of Lyapunov function, we propose a method to certify almost global stability of an equilibrium on a hypertorus. We show that the proposed method can certify robustness of phase synchronization of all-to-all and weakly coupled limit cycle oscillators with respect to disturbances in phases. The method leverages sum of squares polynomial optimization to construct the certification function.
Keywords
almost global synchronization, coupled phase oscillators, Lyapunov density
Subject
Engineering, Control and Systems Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.