4.7 Article

Partial Exponential Stability Analysis of Slow-Fast Systems via Periodic Averaging

期刊

IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 67, 期 10, 页码 5479-5486

出版社

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3117151

关键词

Stability criteria; Synchronization; Laser stability; Oscillators; Circuit stability; Control theory; Asymptotic stability; Averaging; Kuramoto-Sakaguchi; partial exponen tial stability; remote synchronization

资金

  1. European Research Council [ERC-CoG-771687]
  2. Netherlands Organization for Scientific Research [NWO-vidi-14134]
  3. Australian Research Council (ARC) [DP-190100887, DP-160104500]
  4. Data61-CSIRO

向作者/读者索取更多资源

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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