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Consensus problem in directed networks of multi-agents via nonlinear protocols. (English) Zbl 1233.34012
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:
34B45 Boundary value problems on graphs and networks for ordinary differential equations
15A39 Linear inequalities of matrices
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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References:
[1] Gazi, V., IEEE trans. syst. man cybern. B, 38, 267, (2008)
[2] Saber, R., IEEE trans. automat. control, 51, 401, (2006)
[3] Pecora, L.; Carroll, T., Phys. rev. lett., 80, 2109, (1998)
[4] Zhou, C.; Motter, A.; Kurths, J., Phys. rev. lett., 96, 034101, (2006)
[5] Nishikawa, T.; Motter, A.E., Phys. rev. E, 73, 065106, (2006)
[6] Nishikawa, T.; Motter, A.E., Physica D, 224, 77, (2006)
[7] Restrepo, J.G.; Hunt, B.R.; Ott, E., Phys. rev. E, 71, 036151, (2005)
[8] Restrepo, J.G.; Ott, E.; Hunt, B.R., Chaos, 16, 015107, (2006)
[9] Wu, W.; Chen, T., Nonlinearity, 20, 789, (2007)
[10] Yu, W.; Cao, J.; Yuan, L., Phys. lett. A, 372, 4438, (2008)
[11] Duan, Z.; Chen, G.; Huang, L., Phys. lett. A, 372, 3741, (2008)
[12] Vicsek, T.; Cziroók, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Phys. rev. lett., 75, 1226, (1995)
[13] Saber, R.; Murray, R., IEEE trans. automat. control, 49, 1520, (2004)
[14] Jadbabaie, A.; Lin, J.; Morse, A., IEEE trans. automat. control, 48, 988, (2003)
[15] Moreau, L., IEEE trans. automat. control, 50, 169, (2005)
[16] Ren, W.; Beard, R., IEEE trans. automat. control, 50, 655, (2005)
[17] Lu, W.; Chen, T., Physica D, 198, 148, (2004)
[18] Lu, W.; Atay, F.; Jost, J., SIAM J. math. anal., 39, 1231, (2007)
[19] Bauso, D.; Giarré, L.; Pesenti, R., Syst. control lett., 55, 918, (2006)
[20] Barbarossa, S.; Scutari, G., IEEE trans. signal process., 55, 3456, (2007)
[21] Chen, T.; Zhu, Z., Int. J. bifur. chaos, 17, 999, (2007)
[22] Lu, W.; Chen, T., IEEE trans. circuits syst.-I, 51, 2491, (2004)
[23] Liu, X.; Chen, T., Physica A, 381, 82, (2007)
[24] Hui, Q.; Haddad, W., Automatica, 44, 2375, (2008)
[25] Liu, X.; Chen, T., Physica A, 387, 4429, (2008)
[26] Cortés, J., Automatica, 44, 726, (2008)
[27] Lu, W.; Chen, T., Physica D, 213, 214, (2006)
[28] Lu, W.; Chen, T.; Chen, G., Physica D, 221, 118, (2006)
[29] Chen, T.; Liu, X.; Lu, W., IEEE trans. circuits syst.-I, 54, 1317, (2007)
[30] Jiang, F.; Wang, L., Physica D, 238, 1550, (2009)
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