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               have also presented simulation results to illustrate the effectiveness of our approach.

               In future work, how to obtain more generalized and sufficient consensus conditions will be considered. Fur-
               ther, we will extend the results presented in this paper to complex inertial systems and topological networks,
               including random and time-delay networks.



               DECLARATIONS
               Authors’ contributions
               Made significant contributions to the research direction and design and conducted theoretical analysis, proof,
               and explanation: Guo Z, Wei C, Shen Y
               Providing administrative, technical, and material support: Yuan W

               Availability of data and materials
               Not applicable.


               Financial support and sponsorship
               This work was supported by the Science and Technology Innovation 2030-Key Project of “New Generation
               Artificial Intelligence” (No. 2018AAA0102403) and the National Natural Science Foundation of China under
               grants (No. T2121003, No. U20B2071, No. 91948204, and No. U19B2033).


               Conflicts of interest
               All authors declared that there are no conflicts of interest.


               Ethical approval and consent to participate
               Not applicable.


               Consent for publication
               Not applicable.

               Copyright
               © The Author(s) 2023.


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