期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 54, 期 2, 页码 353-357出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2008.2007884
关键词
Cooperative control; exponential stabilization; Kuramoto oscillators; multi-agent systems; synchronization
资金
- Office of Naval Research [N00014-02-1-0011, N00014-05-1-0186]
- National Science Foundation [ECS-0122412, HS-0233314, CCR-0209202]
In this technical note we study the problem of exponential synchronization for one of the most popular models of coupled phase oscillators, the Kuramoto model. We consider the special case of finite oscillators with distinct, bounded natural frequencies. Our first result derives a lower bound on the coupling gain which is necessary for the onset of synchronization. This bound improves the one derived by Jadbabaie et al. [8]. We then calculate a lower bound on the coupling gain that is sufficient to guarantee oscillator synchronization and derive further sufficient conditions to ensure exponential synchronization of the angular frequencies of all oscillators to the mean natural frequency of the group. We also characterize the coupling gain that is sufficient for the oscillator phase differences to approach any desired compact set in finite time.
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