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**On the general consensus protocol in multiagent networks with double-integrator dynamics and coupling time delay.**
*(English)*
Zbl 1271.93008

Summary: This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

### MSC:

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

05C90 | Applications of graph theory |

34C23 | Bifurcation theory for ordinary differential equations |

93B60 | Eigenvalue problems |

### Keywords:

consensus algorithm; multiple agents in a directed network; algebraic graph theory; matrix theory; distribution of the eigenvalues
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\textit{T. Dong} and \textit{X. Liao}, Abstr. Appl. Anal. 2013, Article ID 590894, 6 p. (2013; Zbl 1271.93008)

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### References:

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