Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Certification of Almost Global Phase Synchronization of Coupled Oscillators

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. 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. Preprints 2022, 2022080422. 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

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