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

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 <inline-formula><math xmlns=&qu...

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Autores principales:	Tong Yuan, Hongli Yang, Ivan Ganchev Ivanov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	generalized fractional derivatives positive linear electrical circuits systems reachability observability <i>ρ</i>-Laplace transform Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/036d7754f3ed49edbfdc9eda5d1bea8c
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spelling	oai:doaj.org-article:036d7754f3ed49edbfdc9eda5d1bea8c2021-11-25T18:16:35ZReachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives10.3390/math92228562227-7390https://doaj.org/article/036d7754f3ed49edbfdc9eda5d1bea8c2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2856https://doaj.org/toc/2227-7390Positive 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-Laplace transform of <i>f</i> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-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.Tong YuanHongli YangIvan Ganchev IvanovMDPI AGarticlegeneralized fractional derivativespositive linear electrical circuits systemsreachabilityobservability<i>ρ</i>-Laplace transformMathematicsQA1-939ENMathematics, Vol 9, Iss 2856, p 2856 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	generalized fractional derivatives positive linear electrical circuits systems reachability observability <i>ρ</i>-Laplace transform Mathematics QA1-939
spellingShingle	generalized fractional derivatives positive linear electrical circuits systems reachability observability <i>ρ</i>-Laplace transform Mathematics QA1-939 Tong Yuan Hongli Yang Ivan Ganchev Ivanov Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives
description	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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-Laplace transform of <i>f</i> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-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.
format	article
author	Tong Yuan Hongli Yang Ivan Ganchev Ivanov
author_facet	Tong Yuan Hongli Yang Ivan Ganchev Ivanov
author_sort	Tong Yuan
title	Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives
title_short	Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives
title_full	Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives
title_fullStr	Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives
title_full_unstemmed	Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives
title_sort	reachability and observability of positive linear electrical circuits systems described by generalized fractional derivatives
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/036d7754f3ed49edbfdc9eda5d1bea8c
work_keys_str_mv	AT tongyuan reachabilityandobservabilityofpositivelinearelectricalcircuitssystemsdescribedbygeneralizedfractionalderivatives AT hongliyang reachabilityandobservabilityofpositivelinearelectricalcircuitssystemsdescribedbygeneralizedfractionalderivatives AT ivanganchevivanov reachabilityandobservabilityofpositivelinearelectricalcircuitssystemsdescribedbygeneralizedfractionalderivatives
_version_	1718411359214895104

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

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