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On the stability of linear systems with fractional-order elements

Author

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  • Radwan, A.G.
  • Soliman, A.M.
  • Elwakil, A.S.
  • Sedeek, A.

Abstract

Linear integer-order circuits are a narrow subset of rational-order circuits which are in turn a subset of fractional-order. Here, we study the stability of circuits having one fractional element, two fractional elements of the same order or two fractional elements of different order. A general procedure for studying the stability of a system with many fractional elements is also given. It is worth noting that a fractional element is one whose impedance in the complex frequency s-domain is proportional to sα and α is a positive or negative fractional-order. Different transformations and methods will be illustrated via examples.

Suggested Citation

  • Radwan, A.G. & Soliman, A.M. & Elwakil, A.S. & Sedeek, A., 2009. "On the stability of linear systems with fractional-order elements," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2317-2328.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2317-2328
    DOI: 10.1016/j.chaos.2007.10.033
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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. Lu, Jun Guo, 2006. "Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 519-525.
    3. Yan, Jianping & Li, Changpin, 2007. "On chaos synchronization of fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 725-735.
    4. Lu, Jun Guo, 2005. "Chaotic dynamics and synchronization of fractional-order Arneodo’s systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1125-1133.
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    Cited by:

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    2. Abir Lassoued & Olfa Boubaker, 2017. "Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms," Complexity, Hindawi, vol. 2017, pages 1-10, October.
    3. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    4. Palanivel, J. & Suresh, K. & Sabarathinam, S. & Thamilmaran, K., 2017. "Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 33-41.
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    6. Mishra, Shalabh Kumar & Upadhyay, Dharmendra Kumar & Gupta, Maneesha, 2018. "An approach to improve the performance of fractional-order sinusoidal oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 126-135.

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