This paper considers the mean‐square bounded consensus of heterogeneous discrete‐time multi‐agent systems with noise over fixed and Markov switching topologies. Firstly, a protocol is designed based on the agents' neighbor information with noise. Secondly, by using the Lyapunov function method, matrix analysis and probability theory, sufficient conditions for the mean‐square bounded consensus are given. Finally, several simulations are presented to illustrate the potential correctness of the results.

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