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Zbl 1233.34012
Liu, Xiwei; Chen, Tianping; Lu, Wenlian
Consensus problem in directed networks of multi-agents via nonlinear protocols. (English)
[J] Phys. Lett., A 373, No. 35, 3122-3127 (2009). ISSN 0375-9601

Summary: In this letter, the consensus problem via distributed nonlinear protocols for directed networks is investigated. Its dynamical behaviors are described by Ordinary Differential Equations (ODEs). Based on graph theory, matrix theory and the Lyapunov direct method, some sufficient conditions of nonlinear protocols guaranteeing asymptotic or exponential consensus are presented and rigorously proved. For nonlinearly coupled networks, we generalize the results for undirected networks to directed networks. Consensus under pinning control technique is also developed here. Some simulations show the validity of the theories.

MSC 2000:: *34B45 Boundary value problems on graphs and networks
15A39 Linear inequalities
34D08 Lyapunov exponents

Keywords: consensus; distributed control; nonlinear protocol; directed graphs; spanning tree; asymptotic or exponential consensus ; pinning control

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