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Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives

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  • Tong Yuan

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Hongli Yang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Ivan Ganchev Ivanov

    (Faculty of Economics and Business Administration, Sofia University “St. Kl. Ohridski”, 125 Tzarigradsko Chaussee Blvd., Bl. 3, 1113 Sofia, Bulgaria)

Abstract

Positive linear electrical circuits systems described by generalized fractional derivatives are studied in this paper. We mainly focus on the reachability and observability of linear electrical circuits systems. Firstly, generalized fractional derivatives and ρ -Laplace transform of f is presented and some preliminary results are provided. Secondly, the positivity of linear electrical circuits systems described by generalized fractional derivatives is investigated and conditions for checking positivity of the systems are derived. Thirdly, reachability and observability of the generalized fractional derivatives systems are studied, in which the ρ -Laplace transform of a Mittag-Leffler function plays an important role. At the end of the paper, illustrative electrical circuits systems are presented, and conclusions of the paper are presented.

Suggested Citation

  • Tong Yuan & Hongli Yang & Ivan Ganchev Ivanov, 2021. "Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives," Mathematics, MDPI, vol. 9(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2856-:d:676320
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    References listed on IDEAS

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    1. Khan, Hasib & Jarad, Fahd & Abdeljawad, Thabet & Khan, Aziz, 2019. "A singular ABC-fractional differential equation with p-Laplacian operator," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 56-61.
    2. Sene, Ndolane & Abdelmalek, Karima, 2019. "Analysis of the fractional diffusion equations described by Atangana-Baleanu-Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 158-164.
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