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New methods to realize the cluster consensus for multi‐agent networks

This paper investigates the cluster consensus problem for multi‐agent networks via a new method. Firstly, a distributed cluster consensus protocol is proposed by constructing a new Laplacian matrix, which is not required to be row‐zero‐sum. It is shown that the cluster consensus of directed multi‐agent networks can be achieved under the presented protocol, and the final cluster consensus values of the considered system are also given in this paper, which only depend on the initial states of all agents. Next, a pinning cluster consensus law is provided to force the dynamics of the agents to the desired trajectory. Furthermore, it is found that the cluster consensus of directed networks can be reached even in presence of arbitrary finite communication delays. Finally, effectiveness of the obtained results is demonstrated by numerical examples.