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Group consensus of discrete-time multi-agent systems with fixed and stochastic switching topologies

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Abstract

This paper investigates the group consensus problem for discrete-time multi-agent systems with a fixed topology and stochastic switching topologies. The stochastic switching topologies are assumed to be governed by a finite-time Markov chain. The group consensus problem of the multi-agent systems is converted into the stability problem of the error systems by a model transformation. Based on matrix theory and linear system theory, we obtain two necessary and sufficient conditions of couple-group consensus for the case of fixed topology, and one necessary and sufficient condition of mean-square couple-group consensus for the case of stochastic switching topologies. Algorithms are provided to design the feasible control gains. Then, the results are extended to the case of multi-group consensus. Finally, simulation examples are given to show the effectiveness of the proposed results.

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Acknowledgments

The work of J.H. Park was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2A10005201). Also, the work of H. Zhao was supported by the National Natural Science Foundation of China under Grants nos. 61203056, 61104007.

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Authors and Affiliations

  1. Faculty of Electronic and Electrical Engineering, Huaiyin Institute of Technology, Huai’an, 223003, Jiangsu, People’s Republic of China

    Huanyu Zhao

  2. Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan, 712-749, Republic of Korea

    Huanyu Zhao & Ju H. Park

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  1. Huanyu Zhao
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  2. Ju H. Park
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Correspondence to Ju H. Park.

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Zhao, H., Park, J.H. Group consensus of discrete-time multi-agent systems with fixed and stochastic switching topologies. Nonlinear Dyn 77, 1297–1307 (2014). https://doi.org/10.1007/s11071-014-1379-0

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  • DOI: https://doi.org/10.1007/s11071-014-1379-0

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