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On average consensus in directed networks of agents with switching topology and time delay. (English) Zbl 1260.93003
Summary: In this article, the average consensus problem in directed networks of agents with both switching topology and coupling delay is investigated. First, based on a specific orthogonal transformation of the Laplacian matrix, an important proposition for verifying the positive definiteness of a class of quadratic forms is provided, which is of independent interest in matrix theory. The relation between weakly connected and strongly connected digraphs is also investigated. Then, it is proved that all the agents reach the average consensus asymptotically for appropriate time delay if the communication topology keeps weakly connected and balanced. Finally, a numerical example is given to demonstrate the effectiveness and advantage of the new result.

93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
Full Text: DOI
[1] DOI: 10.1007/s00498-006-0006-0 · Zbl 1117.93058
[2] DOI: 10.1016/j.automatica.2007.12.010 · Zbl 1283.93013
[3] Cao Y, International Journal of Robust Nonlinear Control (2009)
[4] DOI: 10.1109/TAC.2004.834433 · Zbl 1365.90056
[5] DOI: 10.1007/978-1-4613-0163-9
[6] Gouaisbaut F, Proceedings of the 5th IFAC Symposium Robust Control Design (2006)
[7] DOI: 10.1109/TAC.2003.812781 · Zbl 1364.93514
[8] DOI: 10.1016/j.automatica.2009.09.002 · Zbl 1192.93013
[9] Lee, D and Spong, M. Agreement with Non-uniform Information Delays. Proceedings of the American Control Conference. 2006, Minneapolis, MN. pp.756–761.
[10] DOI: 10.1016/j.physa.2007.08.040
[11] Moreau, L. Stability of Continuous-time Distributed Consensus Algorithms. Proceedings of the IEEE Conference Decision Control. 2004. pp.3998–4003. Paradise Island, Bahamas
[12] DOI: 10.1109/TAC.2004.841888 · Zbl 1365.93268
[13] DOI: 10.1109/JPROC.2006.887293 · Zbl 1376.68138
[14] DOI: 10.1109/TAC.2004.834113 · Zbl 1365.93301
[15] Qin, J, Gao, H and Zheng, WX. Second-order Consensus for Networks of Agents with Fixed and Switching Topology. Proceedings of the Joint 48th IEEE Conference on Decision Control and 28th Chinese Control Conference. 2009. pp.883–888. Shanghai, China
[16] DOI: 10.1109/TAC.2005.846556 · Zbl 1365.93302
[17] DOI: 10.1016/j.sysconle.2007.08.009 · Zbl 1133.68412
[18] Tanner, HG and Christodoulakis, DK. State Synchronization in Local Interaction Networks is Robust with Respect to Time Delays. Proceeding of the IEEE Conference Decision Control. 2005. pp.4945–4950. Seville, Spain
[19] DOI: 10.1103/PhysRevLett.75.1226
[20] DOI: 10.1080/00207170600825097 · Zbl 1330.94022
[21] DOI: 10.1080/00207720902974603 · Zbl 1175.93166
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