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**Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation.**
*(English)*
Zbl 1255.93010

Summary: By introducing delayed state compensation into the normal asynchronously-coupled consensus algorithm, a new consensus algorithm is constructed to solve the dynamical consensus problem of second-order multi-agent systems with communication delay. Based on frequency-domain analysis, a sufficient and necessary condition, which depends on the communication delay and the control parameters, is obtained for two coupled second-order dynamic agents converging to the dynamical consensus, and it is proved that the proposed algorithm can tolerate higher communication delay than the synchronously-coupled consensus algorithm. According to linear fractional transformation and the small-gain theorem, sufficient conditions are gained for second-order multi-agent systems with communication delay under a general digraph. Simulation results illustrates the correctness of our method.

### MSC:

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

93C80 | Frequency-response methods in control theory |

### Keywords:

second-order multi-agent systems; consensus; communication delay; delayed state compensation
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\textit{C.-L. Liu} and \textit{F. Liu}, Syst. Control Lett. 61, No. 12, 1235--1241 (2012; Zbl 1255.93010)

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### References:

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