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Contraction analysis for fractional-order nonlinear systems

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  • González-Olvera, Marcos A.
  • Tang, Yu

Abstract

In this work we present a novel platform for analysis of fractional-order nonlinear systems that, from a differential analysis as well as contraction analysis point of view, gives the sufficient conditions for the mutual convergence of nearby trajectories whose distance decrease asymptotically bounded by a Mittag-Leffler vanishing function. Particular cases, such as partial contraction and contraction to a linear manifold are studied. Applications to stability analysis, adaptive control, observer design and synchronization of chaotic fractional-order systems are derived in order to demonstrate the effectiveness of the proposed paradigm.

Suggested Citation

  • González-Olvera, Marcos A. & Tang, Yu, 2018. "Contraction analysis for fractional-order nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 255-263.
    • Handle: RePEc:eee:chsofr:v:117:y:2018:i:c:p:255-263
    DOI: 10.1016/j.chaos.2018.10.030
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    References listed on IDEAS

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    1. Lu, Jun Guo, 2005. "Chaotic dynamics and synchronization of fractional-order Arneodo’s systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1125-1133.
    2. Xiong, Xiaohua & Wang, Jinlian & Zhou, Tianshou, 2007. "Contraction principle and its applications in synchronization of nonlinearly coupled systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1147-1153.
    3. Gao, Xin & Yu, Juebang, 2005. "Synchronization of two coupled fractional-order chaotic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 141-145.
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    Cited by:

    1. Ghosh, Uttam & Pal, Swadesh & Banerjee, Malay, 2021. "Memory effect on Bazykin’s prey-predator model: Stability and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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