Determination of minimal realisation of one-dimensional continuous-time fractional linear system

In this paper, a new alternative method for the determination of the set of all minimal positive and non-positive realisations of the one-dimensional fractional continuous-time linear systems based on the one-dimensional digraphs theory has been presented. In addition, all realisations in the set are minimal. For the proposed method, an algorithm was also constructed. The algorithm is based on a parallel computing method to gain needed speed and computational power for such a solution. The proposed method is discussed and illustrated with numerical examples.

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