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

Markowski, K. A.

International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 1, pp. 9-24.

Résumé

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.

Détail

Keywords: fractional system, positive system, descriptor system, digraph structure, digraph mask
Mots-clés : układ ułamkowy, układ dodatni, układ deskryptorowy

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