On Exponential Synchronization of Kuramoto Oscillators

被引：350

作者：

Chopra, Nikhil ^{[1
,2
]}

Spong, Mark W. ^{[3
]}

机构：

[1] Univ Maryland, Dept Mech Engn, College Pk, MD 20742 USA

[2] Univ Maryland, Syst Res Inst, College Pk, MD 20742 USA

[3] Univ Texas Dallas, Erik Jonsson Sch Engn & Comp Sci, Richardson, TX 75080 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2009年 / 54卷 / 02期

基金：

美国国家科学基金会;

关键词：

Cooperative control; exponential stabilization; Kuramoto oscillators; multi-agent systems; synchronization; MODEL; STABILITY; LOCKING; AGENTS;

D O I：

10.1109/TAC.2008.2007884

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：353 / 357

页数：5

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