<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure

Published Online: Mar 31, 2018

Page range: 9 - 24

Received: Feb 05, 2017

Accepted: Aug 09, 2017

DOI: https://doi.org/10.2478/amcs-2018-0001

Keywords
fractional system, positive systems, descriptor systems, realization, digraph structure, digraph mask, algorithm

© by Konrad Andrzej Markowski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure

Published Online: Mar 31, 2018

Page range: 9 - 24

Received: Feb 05, 2017

Accepted: Aug 09, 2017

DOI: https://doi.org/10.2478/amcs-2018-0001

Keywordsfractional system, positive systems, descriptor systems, realization, digraph structure, digraph mask, algorithm

© by Konrad Andrzej Markowski

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
fractional system, positive systems, descriptor systems, realization, digraph structure, digraph mask, algorithm