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Consensus problem of networked multi-agent systems with constant communication delay: stochastic switching topology case. (English) Zbl 1417.93284

Summary: This article proposes an observer-based control strategy for networked multi-agent systems with constant communication delay and stochastic switching topology. First, using the system transformation method, the mean-square consensus problem of multi-agent systems can be converted into the mean-square stability problem of an equivalent system, and some equivalent conditions concerning the mean-square consensus are presented. Then, an example is given to illustrate that the connection weights should be regarded as the parameters to be designed, since they have a great effect on the mean-square consensus of multi-agent systems. By choosing appropriate connection weights, the mean-square consensus problem can be converted into the mean-square stabilisation problem of N-1 delay systems with stochastic switching signal, whose related observer-based stabilisability criteria can be established in the form of linear matrix inequalities (LMIs). Furthermore, if the LMIs are feasible, the multi-agent systems achieve mean-square consensus if and only if the union of graphs in the switching topology set has a directed spanning tree. Finally, numerical simulations are given to illustrate our results.

MSC:

93D99 Stability of control systems
93A14 Decentralized systems
68T42 Agent technology and artificial intelligence
93E03 Stochastic systems in control theory (general)
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