Mean-square consensus of hybrid multi-agent systems with noise and nonlinear 
terms over jointly connected topologies

Sun, Fenglan; Lu, Chuan; Zhu, Wei; Kurths, Jürgen

doi:10.1016/j.jfranklin.2023.03.031

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Mean-square consensus of hybrid multi-agent systems with noise and nonlinear terms over jointly connected topologies

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Sun, Fenglan
External Organizations;

Lu, Chuan
External Organizations;

Zhu, Wei
External Organizations;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

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Sun, F., Lu, C., Zhu, W., Kurths, J. (2023): Mean-square consensus of hybrid multi-agent systems with noise and nonlinear terms over jointly connected topologies. - Journal of the Franklin Institute, 360, 8, 5759-5779.
https://doi.org/10.1016/j.jfranklin.2023.03.031

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This paper studies the mean-square consensus of second-order hybrid multi-agent systems over jointly connected topologies. Systems with time-varying delay and multiplicative noise are considered. The date sampling control technique is adopted. Through matrix transformation, a positive definite matrix transformed by the Laplacian matrix is obtained, where the Laplacian matrix is a connected subgraph divided by the jointly connected topologies. By using graph theory, matrix theory and Lyapunov stability theory, sufficient conditions and the upper bound of time delays for the mean-square consensus are obtained. Finally, several simulations are presented to demonstrate the validity of the control method.