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http://www.77cn.com.cnRazumikhin function (rather than the stochastic matrix related to graph theory) was employed in the stability analysis. Numerical examples were given to illustrate the theoretical results.

7Figure 2 Interconnection topology G3 for four agents

Acknowledgment

The author would like to thank Prof. Yiguang Hong at Institute of Systems Science, Chinese Academy of Sciences and Prof. Xiaoming Hu at Royal Institute of Technology, Sweden, for discussions about some parts in this work. The author would also like to thank the associated editor and the anonymous reviewers for their insightful comments and suggestions.

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References

[1] KURAMOTO Y.:‘Cooperative dynamics of oscillator community’, Prog. Theor. Phys. Suppl., 1984, 79, pp. 223– 240[2] STROGATZ S.H.:‘From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators’, Physica D, 2000, 143, pp. 1– 20[3] GAZI V., PASSINO K.M.:‘Stability analysis of social foraging swarms’, IEEE Trans. Syst., Man, Cyber., Part B: Cyber., 2004, 34, pp. 539– 557[4] JADBABAIE A., LIN J., MORSE A.S.:‘Coordination of groups of mobile agents using nearest neighbor rules’, IEEE Trans. Autom. Control, 2003, 48, (6), pp. 988– 1001[5] GAZI V., PASSINO K.M.:‘Stability analysis of swarms’, IEEE Trans. Autom. Control, 2003, 48, (4), pp. 692– 697[6] OLFATI-SABER R., MURRAY R.M.:‘Consensus problems in networks of agents with switching topology and timedelays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 1520– 1533[7] BLIMAN P.-A., FERRARI-TRECATE G.:‘Average consensus problems in networks of agents with delayed communications’, Automatica, 2008, 44, pp. 1985– 1995[8] LIN P., JIA Y.:‘Average consensus in networks of multiagents with both switching topology and coupling timedelay’, Physica A, 2008, 387, pp. 303– 313[9] XIAO F., WANG L.:‘Consensus problems for highdimensional multi-agent systems’, IET Contr. Theory Appl., 2007, 1, (3), pp. 830– 837[10] LOW S., PAGANINI F., DOYLE J.:‘Internet congestion control’, IEEE Control Syst. Mag., 2002, 32, (1), pp. 28– 43 117

Figure 3 Position evolutions

Figure 4 Velocity evolutions

Fig. 4, we also nd that the velocity of each agent will approach the average of the initial values, that is, P vi (t) ! 1=4 4 vj (0)¼ vü[0:125, 0:125]T as t ! 1. j¼1

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Conclusions

The paper addressed delayed consensus problem of a group of leaderless multiple mobile agents with neighbour-based rule. The consensus stability was guaranteed with both xed and switched interconnection topologies of the considered multi-agent system. The dynamic

s of each agent was second order with time-varying delays and Lyapunov– IET Control Theory Appl., 2010, Vol. 4, Iss. 1, pp. 109– 118 doi: 10.1049/iet-cta.2008.0479

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