Digraphs Minimal Realisations of State Matrices for Fractional Positive Systems

This paper presents a method of the determination of characteristic polynomial realisations of the fractional positive system. The algorithm finds a complete set of all possible realisations instead of only a few realisations. In addition, all realisations in the set are minimal. The proposed method uses a parallel computing algorithm based on a digraphs theory which is used to gain much needed speed and computational power for a numeric solution. The presented procedure has been illustrated with a numerical example.