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Paper details
Number 1 - March 2018
Volume 28 - 2018
Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure
Konrad Andrzej Markowski
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.
Keywords
fractional system, positive systems, descriptor systems, realization, digraph structure, digraph mask, algorithm