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Consensus of Multiagent Systems Described by Various Noninteger Derivatives

Author

Listed:
  • G. Nava-Antonio
  • G. Fernández-Anaya
  • E. G. Hernández-Martínez
  • J. J. Flores-Godoy
  • E. D. Ferreira-Vázquez

Abstract

In this paper, we unify and extend recent developments in Lyapunov stability theory to present techniques to determine the asymptotic stability of six types of fractional dynamical systems. These differ by being modeled with one of the following fractional derivatives: the Caputo derivative, the Caputo distributed order derivative, the variable order derivative, the conformable derivative, the local fractional derivative, or the distributed order conformable derivative (the latter defined in this work). Additionally, we apply these results to study the consensus of a fractional multiagent system, considering all of the aforementioned fractional operators. Our analysis covers multiagent systems with linear and nonlinear dynamics, affected by bounded external disturbances and described by fixed directed graphs. Lastly, examples, which are solved analytically and numerically, are presented to validate our contributions.

Suggested Citation

  • G. Nava-Antonio & G. Fernández-Anaya & E. G. Hernández-Martínez & J. J. Flores-Godoy & E. D. Ferreira-Vázquez, 2019. "Consensus of Multiagent Systems Described by Various Noninteger Derivatives," Complexity, Hindawi, vol. 2019, pages 1-14, February.
    • Handle: RePEc:hin:complx:3297410
    DOI: 10.1155/2019/3297410
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    References listed on IDEAS

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    1. S. Sepehr Tabatabaei & Mohammad Javad Yazdanpanah & Sajad Jafari & Julien Clinton Sprott, 2014. "Extensions in dynamic models of happiness: effect of memory," International Journal of Happiness and Development, Inderscience Enterprises Ltd, vol. 1(4), pages 344-356.
    2. Hamed Taghavian & Mohammad Saleh Tavazoei, 2018. "Stability analysis of distributed-order nonlinear dynamic systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 523-536, February.
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