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Stability analysis of distributed-order nonlinear dynamic systems

Author

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  • Hamed Taghavian
  • Mohammad Saleh Tavazoei

Abstract

The problem of asymptotic stability analysis of equilibrium points in nonlinear distributed-order dynamic systems with non-negative weight functions is considered in this paper. The Lyapunov direct method is extended to be used for this stability analysis. To this end, at first, a discretisation scheme with convergence property is introduced for distributed-order dynamic systems. Then, on the basis of this tool, Lyapunov theorems are proved for asymptotic stability analysis of equilibrium points in distributed-order systems. As the order weight function assumed for the distributed-order systems is general enough, the results are applicable to a wide range of nonlinear distributed-order systems such as fractional-order systems with multiple fractional derivatives. To verify the applicability of the obtained results, these results are applied for the stability analysis of a distributed-order diffusion system and control of a fractional-order Lorenz system with multiple fractional derivatives.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:3:p:523-536
    DOI: 10.1080/00207721.2017.1412535
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    Cited by:

    1. Aadhithiyan, S. & Raja, R. & Zhu, Q. & Alzabut, J. & Niezabitowski, M. & Lim, C.P., 2021. "Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. 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.

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