Two Cases of Digraph Structures Corresponding to Minimal Positive Realisation of Fractional Continuous-Time Linear Systems of Commensurate Order - Markowski, Konrad Andrzej (Journal of Applied Nonlinear Dynamics, 2026)
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.