Geodesic
Consensus seeking in multi-agent systems with an active leader and communication delays
Kybernetika, Tome 47 (2011) no. 5, pp. 773-789.

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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 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.
Classification : 62A10, 93E12
Keywords: multi-agent system; consensus; leader-following; time-delay 
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     author = {Gao, Lixin and Tang, Yutao and Chen, Wenhai and Zhang, Hui},
     title = {Consensus seeking in multi-agent systems with an active leader and communication delays},
     journal = {Kybernetika},
     pages = {773--789},
     publisher = {mathdoc},
     volume = {47},
     number = {5},
     year = {2011},
     mrnumber = {2850463},
     zbl = {1236.93006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_5_a8/}
}
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Gao, Lixin; Tang, Yutao; Chen, Wenhai; Zhang, Hui. Consensus seeking in multi-agent systems with an active leader and communication delays. Kybernetika, Tome 47 (2011) no. 5, pp. 773-789. http://geodesic.mathdoc.fr/item/KYB_2011__47_5_a8/