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Necessary and sufficient conditions for mean square consensus under Markov switching topologies. (English) Zbl 1307.93474
Summary: This article deals with the mean square consensus problem for second-order discrete-time multi-agent systems. Both cases of systems with and without time delays in Markov switching topologies are considered. With the introduced control protocols, necessary and sufficient conditions for mean square consensus of second-order multi-agent systems are derived. Under the given control protocols in Markov switching topologies, the second-order multi-agent systems can reach mean square consensus if and only if each union of the graphs corresponding to all the nodes in closed sets has a spanning tree. Finally, a simulation example is provided to illustrate the effectiveness of our theoretical results.

MSC:
93E24 Least squares and related methods for stochastic control systems
93A14 Decentralized systems
93C55 Discrete-time control/observation systems
68T42 Agent technology and artificial intelligence
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