fractional systems ; positive systems ; descriptor systems ; realization ; digraph structure ; digraph mask ; algorithm
Abstract:In the last two decades, fractional calculus has become a subject of great interest in various areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned by Leibniz and L`Hospital. Fractional calculus has been found to be a very useful tool for modeling linear systems. In this paper, a method for computation of a set of a minimal positive realization of a given transfer function of linear fractional continuous-time descriptor systems has been presented. ; The proposed method is based on digraph theory. Also, two cases of a possible input-output digraph structure are investigated and discussed. It should be noted that a digraph mask is introduced and used for the first time to solve a minimal positive realization problem. For the presented method, an algorithm was also constructed. The proposed solution allows minimal digraph construction for any one-dimensional fractional positive system. The proposed method is discussed and illustrated in detail with some numerical examples.
Publisher:Zielona Góra: Uniwersytet Zielonogórski
Date: Resource Type: DOI: Pages: Source:AMCS, volume 28, number 1 (2018) ; click here to follow the link
Language: License CC BY 4.0: Rights: