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

Tong Yuan, Hongli Yang and Ivan Ganchev Ivanov
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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

Mathematics, 2021, vol. 9, issue 22, 1-16

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 ? -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 ? -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.

Keywords: generalized fractional derivatives; positive linear electrical circuits systems; reachability; observability; ? -Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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