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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Two Cases of Digraph Structures Corresponding to Minimal Positive Realisation of Fractional Continuous-Time Linear Systems of Commensurate Order

Journal of Applied Nonlinear Dynamics 6(2) (2017) 265--282 | DOI:10.5890/JAND.2017.06.011

Konrad Andrzej Markowski

Faculty of Electrical Engineering, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

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Abstract

The positive and minimal realisation problem for fractional continuous-time linear single-input and single-output (SISO) systems is formulated. Method based on the one-dimensional digraph for finding a positive and minimal realisation of a given proper transfer function is proposed. Two special cases of the digraph structure are given. Sufficient conditions for the existence of a positive minimal realisation of a given proper transfer function systems are established. The algorithm for computation of a positive minimal realisation is proposed and illustrated with a numerical example. The algorithm is based on a parallel computing method to gain needed speed and computational power for such a solution.

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