Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 67, Issue 10, Pages 5479-5486Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3117151
Keywords
Stability criteria; Synchronization; Laser stability; Oscillators; Circuit stability; Control theory; Asymptotic stability; Averaging; Kuramoto-Sakaguchi; partial exponen tial stability; remote synchronization
Funding
- European Research Council [ERC-CoG-771687]
- Netherlands Organization for Scientific Research [NWO-vidi-14134]
- Australian Research Council (ARC) [DP-190100887, DP-160104500]
- Data61-CSIRO
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This article presents new criteria for the partial exponential stability of a slow-fast nonlinear system and applies it to the study of remote synchronization of Kuramoto-Sakaguchi oscillators. Detuning the central mediating oscillator's natural frequency increases synchronization robustness.
This article presents some new criteria for the partial exponential stability of a slow-fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by averaging over this fast scalar variable instead of the time variable. We show that the partial exponential stability of the averaged system implies that of the original one. We then apply the obtained criteria to the study of remote synchronization of Kuramoto-Sakaguchi oscillators coupled by a star network with two peripheral nodes. We show that detuning the natural frequency of the central mediating oscillator increases the robustness of the remote synchronization against phase shifts. This article appears to be the first-known attempt to analytically study the phase-unlocked remote synchronization.
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