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In the current paper, minimum‐energy time‐varying formation design and analysis problems of distributed multi‐agent systems (DMASs) subjected to randomly switching topologies and aperiodic interaction pauses are investigated, which can ensure the time‐varying formation achievement with the minimum‐energy consumption in the sense of the linear matrix inequality. Firstly, a formation control protocol is designed with local information of neighboring agents, where the total energy consumption during the formation process is constructed and the impacts of interaction constraints are imposed. Then, minimum‐energy formation design and analysis criteria of DMASs are presented in terms of the linear matrix inequality tool, which can be checked by the generalized eigenvalue method. Finally, a numerical simulation is shown to verify the effectiveness of the main results.

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