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

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.

Reachability and Observability of Fractional Order Descriptor System

“…This work depends upon the generalized fractional derivatives. Positive electrical linear circuit systems narrated by generalized fractional derivatives are discussed in this work [13]. With the help of the Mittage-Leffler matrix function, we proved some results, as it is the generalization of the exponential function in fractional case, defined as…”

“…We have studied the data in which the ρ−Laplace transform of a Mittag-Leffler function plays a vital role [2]. In this work we are concerned with the reachability and observability of positive electrical linear circuit systems and also concerned with reachability conditions that is reachability matrix and rank conditions [13]. Further, we have discussed reachability and observability using generalized fractional derivatives.…”

Can science exist without free discussion?

“…Until now, I have not noticed it. After the publication of article (Piotrowska, 2018) in the AEE, I noticed two more articles (Piotrowska, 2020;Yuan and Yang, 2021) containing an error. In Piotrowska's (2020) article, under item 23 of the literature list is the author's work (Piotrowska, 2018).…”

“…My critical articles were noticed in the paper (Yuan and Yang, 2021), but I think without proper attention. I will quote an example of an erroneous part of the work (Yuan and Yang, 2021):…”

“…Originally, today's all physics equations, including electrical engineering, are written with the help of differential-integral equations of integer order. Writing them (Piotrowska, 2018; Yuan and Yang, 2021; Ortigueira and Machado, 2018) with the use of fractional order equations is incorrect because there is no formula that allows for an unambiguous transition from the fractional form to the form of integer order equations. Perhaps in the future there will be physics in which all equations will be of fractional order, but this does not seem likely.…”