Certification of Almost Global Phase Synchronization of Coupled Oscillators

Mahmut Kudeyt; Ayşegül Kıvılcım; Elif Köksal Ersöz; Özkan Karabacak

doi:10.20944/preprints202208.0422.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 22 August 2022 / Approved: 24 August 2022 / Online: 24 August 2022 (13:19:50 CEST)

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.

almost global synchronization, coupled phase oscillators, Lyapunov density

Engineering, Control and Systems Engineering

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Certification of Almost Global Phase Synchronization of Coupled Oscillators

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