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**Consensus seeking in multi-agent systems with an active leader and communication delays.**
*(English)*
Zbl 1236.93006

Summary: In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The dynamics of the active leader is given in a general form of a linear system. The switching interconnection topology with communication delay among the agents is taken into consideration. A neighbor-based estimator is designed for each agent to obtain the unmeasurable state variables of the dynamic leader, and then a distributed feedback control law is developed to achieve consensus. The feedback parameters are obtained by solving a Riccati equation. By constructing a common Lyapunov function, some sufficient conditions are established to guarantee that each agent can track the active leader by assumption that interconnection topology is undirected and connected. We also point out that some results can be generalized to a class of directed interaction topologies. Moreover, the Input-to-State Stability (ISS) is obtained for multi-agent system with variable interconnection topology and communication delays in a disturbed environment.

### MSC:

93A14 | Decentralized systems |

93D25 | Input-output approaches in control theory |

93E12 | Identification in stochastic control theory |

68T42 | Agent technology and artificial intelligence |

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