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**Leader-following consensus of second-order agents with multiple time-varying delays.**
*(English)*
Zbl 1205.93056

Summary: A leader-following consensus problem of second-order multi-agent systems with fixed and switching topologies as well as non-uniform time-varying delays is considered. For the case of fixed topology, a necessary and sufficient condition is obtained. For the case of switching topology, a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large. We not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate. An example with simulation is presented to illustrate the theoretical results.

### MSC:

93B52 | Feedback control |

93D20 | Asymptotic stability in control theory |

93C35 | Multivariable systems, multidimensional control systems |

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\textit{W. Zhu} and \textit{D. Cheng}, Automatica 46, No. 12, 1994--1999 (2010; Zbl 1205.93056)

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### References:

[1] | Cheng, D.; Wang, J.; Hu, X., An extension of LaSalle’s invariance principle and its application to multi-agent consensus, IEEE Transactions on Automatic Control, 53, 1765-1770 (2008) · Zbl 1367.93427 |

[2] | Fax, A.; Murray, R., Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control, 49, 1453-1464 (2004) |

[4] | Hu, J.; Hong, Y., Leader-following coordination of multi-agent systems with coupling time delays, Physica A, 374, 853-863 (2007) |

[5] | Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 998-1001 (2003) · Zbl 1364.93514 |

[6] | Lin, P.; Jia, Y., Average consensus in networks of multi-agents with both switching topology and coupling time-delay, Physica A, 387, 303-313 (2008) |

[7] | Lin, P.; Jia, Y., Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies, Automatica, 45, 2154-2158 (2009) · Zbl 1175.93078 |

[8] | Moreau, L., Stability of multi-agent systems with time-dependent communication links, IEEE Transactions on Automatic Control, 50, 169-182 (2005) · Zbl 1365.93268 |

[9] | Peng, K.; Yang, Y., Leader-following consensus problem with a varying-velocity leader and time-varying delays, Physica A, 388, 193-208 (2009) |

[10] | Saber, R.; Murray, R., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 1520-1533 (2004) · Zbl 1365.93301 |

[12] | Sun, Y.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems & Control Letters, 57, 175-183 (2008) · Zbl 1133.68412 |

[13] | Vicsek, T.; Cziroók, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 75, 1226-1229 (1995) |

[14] | Wang, J.; Cheng, D., Stability of switched nonlinear systems via extensions of LaSalle’s invariance principle, Science in China Series F: Information Science, 52, 84-90 (2009) · Zbl 1182.93098 |

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