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On average consensus in directed networks of agents with switching topology and time delay. (English) Zbl 1260.93003
Summary: In this article, the average consensus problem in directed networks of agents with both switching topology and coupling delay is investigated. First, based on a specific orthogonal transformation of the Laplacian matrix, an important proposition for verifying the positive definiteness of a class of quadratic forms is provided, which is of independent interest in matrix theory. The relation between weakly connected and strongly connected digraphs is also investigated. Then, it is proved that all the agents reach the average consensus asymptotically for appropriate time delay if the communication topology keeps weakly connected and balanced. Finally, a numerical example is given to demonstrate the effectiveness and advantage of the new result.

MSC:
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
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