## Distributed $${\delta}$$-consensus in directed delayed networks of multi-agent systems.(English)Zbl 1278.93018

Summary: In this article, we propose a distributed $${\delta}$$-consensus protocol in directed networks of dynamic agents having communication delays. The $${\delta}$$-consensus protocol is an average consensus protocol where agents exchange the information with their neighbors at some discontinuous moments. We provide convergence analysis for such consensus algorithm under stochastic switching communication graphs, and then present some generic criteria for solving the average consensus problem. We also show that directed delayed networks of dynamic agents can achieve average consensus even when each agent in the networks intermittently exchanges the information with its neighbors only at some discrete moments. Subsequently, a typical numerical example illustrates and visualizes the effectiveness and feasibility of the theoretical results.

### MSC:

 93A14 Decentralized systems 68T42 Agent technology and artificial intelligence 93E03 Stochastic systems in control theory (general)
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### References:

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