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**Consensus for multiagent systems with nonlinear dynamics and time delays using a two-hop relay adaptive method.**
*(English)*
Zbl 1406.93016

Summary: This paper investigates the consensus problem for multiagent systems with nonlinear dynamics and time delays. A distributed adaptive consensus protocol is proposed in which the time delays are explicitly included in the adaptive algorithm. It is shown that the resultant closed loop system involves doubly larger time delays, making the stability analysis nontrivial. Stability condition on maximum tolerable time delay is established and controlled by the proposed two-hop adaptive algorithm. The explicit expression of the delay margin is derived and analyzed in the frequency domain. Both the agent state errors and the estimation parameter errors converge to zero. A simulation example is illustrated to verify the theory results.

### MSC:

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

93C10 | Nonlinear systems in control theory |

93C40 | Adaptive control/observation systems |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

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\textit{Q. Cao} et al., Abstr. Appl. Anal. 2014, Article ID 792360, 6 p. (2014; Zbl 1406.93016)

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