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Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer

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  • Cruz-Victoria, Juan C.
  • Martínez-Guerra, Rafael
  • Pérez-Pinacho, Claudia A.
  • Gómez-Cortés, Gian Carlo

Abstract

This paper deals with the master-slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics are considered as the master system and we propose the slave system structure which estimates the unknown state variables. Besides it is introduced a new fractional model free reduced order observer inspired on the new concept of Fractional algebraic observability (FAO); we applied the results to a Rössler hyperchaotic fractional order system and Lorenz fractional order system, and by means of some simulations we show the effectiveness of the suggested approach.

Suggested Citation

  • Cruz-Victoria, Juan C. & Martínez-Guerra, Rafael & Pérez-Pinacho, Claudia A. & Gómez-Cortés, Gian Carlo, 2015. "Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 224-231.
    • Handle: RePEc:eee:apmaco:v:262:y:2015:i:c:p:224-231
    DOI: 10.1016/j.amc.2015.03.120
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    References listed on IDEAS

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    1. Li, Changpin & Yan, Jianping, 2007. "The synchronization of three fractional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 751-757.
    2. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    3. Deng, W.H. & Li, C.P., 2005. "Chaos synchronization of the fractional Lü system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 61-72.
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    1. Cai, Ruiyang & Ge, Fudong & Chen, YangQuan & Kou, Chunhai, 2019. "Regional observability for Hadamard-Caputo time fractional distributed parameter systems," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 190-202.
    2. Zhang, Zhe & Zhang, Jing & Ai, Zhaoyang & Cheng, FanYong & Liu, Feng, 2020. "A novel general stability criterion of time-delay fractional-order nonlinear systems based on WILL Deduction Method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 328-344.
    3. A.G., Soriano–Sánchez & C., Posadas–Castillo & M.A., Platas–Garza & A., Arellano–Delgado, 2018. "Synchronization and FPGA realization of complex networks with fractional–order Liu chaotic oscillators," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 250-262.

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