期刊
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
卷 1, 期 2, 页码 91-106出版社
IEEE COMPUTER SOC
DOI: 10.1109/TNSE.2015.2395075
关键词
Synchronization; contraction of nonlinear systems; stability; consensus
资金
- NIH [1R01GM100473, ONR N00014-13-1-0074, AFOSR FA9550-11-1-0247]
Contraction theory provides an elegant way to analyze the behavior of certain nonlinear dynamical systems. In this paper, we discuss the application of contraction to synchronization of diffusively interconnected components described by nonlinear differential equations. We provide estimates of convergence of the difference in states between components, in the cases of line, complete, and star graphs, and Cartesian products of such graphs. We base our approach on contraction theory, using matrix measures derived from norms that are not induced by inner products. Such norms are the most appropriate in many applications, but proofs cannot rely upon Lyapunov-like linear matrix inequalities, and different techniques, such as the use of the Perron-Frobenious Theorem in the cases of L1 or L1 norms, must be introduced.
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