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Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria

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Abstract

In this manuscript, we are concerned with mixed (discrete and distributed) time-delayed both stability and non-fragile synchronization of nonlinear multi-agent systems (MASs). We shall find stability criteria for the unknown parameter value of nonlinear multi-agent systems using the Lyapunov–Krasovskii functions, Lemma, the analytical techniques, the Kronecker product, and the general specifications for asymptotic stability of selected MASs are obtained. Moreover, criteria for the synchronization of leader–follower unknown parameter value of nonlinear MASs with non-fragile controllers are discussed. At last, we provide two numerical calculations along with the computational simulations to check the validity of the theoretical findings reported in this manuscript.

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Acknowledgements

The article has been written with the joint partial financial support of RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) vide letter No.F.510/8/DRS-I/2016(SAP-I) and DST (FIST-Phase I) vide letter No.SR/FIST/MS-I/2018-17, the National Science Centre in Poland Grant DEC-2017/25/B/ST7/02888 and J. Alzabut would like to thank Prince Sultan University for supporting this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.

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Authors and Affiliations

  1. Department of Mathematics, Alagappa University, Karaikudi, 630 004, India

    A. Stephen

  2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India

    R. Raja

  3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia

    J. Alzabut

  4. Department of Industrial Engineering, OSTİM Technical University, Ankara, 06374, Turkey

    J. Alzabut

  5. School of Mathematics and Statistics, Hunan Normal University, Hunan, 410081, People’s Republic of China

    Quanxin Zhu

  6. Department of Automatic Control and Robotics, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Akademicka 16, Gliwice, 44-100, Poland

    M. Niezabitowski

  7. Department of Electronics, Computing and Mathematics, University of Derby, Derby, UK

    O. Bagdasar

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  1. A. Stephen
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Correspondence to Quanxin Zhu.

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Stephen, A., Raja, R., Alzabut, J. et al. Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria. Neural Process Lett 54, 43–74 (2022). https://doi.org/10.1007/s11063-021-10619-2

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