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Delay-Dependent Stability Region for the Distributed Coordination of Delayed Fractional-Order Multi-Agent Systems

Author

Listed:
  • Abbasali Koochakzadeh

    (Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 1591634311, Iran)

  • Mojtaba Naderi Soorki

    (Department of Electrical Engineering, Sharif University of Technology, Tehran 1458889694, Iran)

  • Aydin Azizi

    (School of Engineering, Computing and Mathematics, Oxford Brookes University, Wheatley Campus, Oxford OX33 1HX, UK)

  • Kamran Mohammadsharifi

    (Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 1591634311, Iran)

  • Mohammadreza Riazat

    (Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran 1543319967, Iran)

Abstract

Delay and especially delay in the transmission of agents’ information, is one of the most important causes of disruption to achieving consensus in a multi-agent system. This paper deals with achieving consensus in delayed fractional-order multi-agent systems (FOMAS). The aim in the present note is to find the exact maximum allowable delay in a FOMAS with non-uniform delay, i.e., the case in which the interactions between agents are subject to non-identical communication time-delays. By proving a stability theorem, the results available for non-delayed networked fractional-order systems are extended for the case in which interaction links have nonequal communication time-delays. In this extension by considering a time-delay coordination algorithm, necessary and sufficient conditions on the time delays and interaction graph are presented to guarantee the coordination. In addition, the delay-dependent stability region is also obtained. Finally, the dependency of the maximum allowable delay on two parameters, the agent fractional-order and the largest eigenvalue of the graph Laplacian matrix, is exactly determined. Numerical simulation results are given to confirm the proposed methodologies.

Suggested Citation

  • Abbasali Koochakzadeh & Mojtaba Naderi Soorki & Aydin Azizi & Kamran Mohammadsharifi & Mohammadreza Riazat, 2023. "Delay-Dependent Stability Region for the Distributed Coordination of Delayed Fractional-Order Multi-Agent Systems," Mathematics, MDPI, vol. 11(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1267-:d:1088861
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    References listed on IDEAS

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    1. Richard L. Magin & Ervin K. Lenzi, 2022. "Fractional Calculus Extension of the Kinetic Theory of Fluids: Molecular Models of Transport within and between Phases," Mathematics, MDPI, vol. 10(24), pages 1-20, December.
    2. Jing Bai & Guoguang Wen & Ahmed Rahmani & Xing Chu & Yongguang Yu, 2016. "Consensus with a reference state for fractional-order multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(1), pages 222-234, January.
    3. Junda Chen & Xuejing Lan & Ye Zhou & Jiaqiao Liang, 2022. "Formation Control with Connectivity Assurance for Missile Swarms by a Natural Co-Evolutionary Strategy," Mathematics, MDPI, vol. 10(22), pages 1-24, November.
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