Digraphs structures corresponding to minimal realisation of fractional continuous-time linear systems with all-pole and all-zero transfer function

In this paper, the new method for computation of a minimal realisation of a given proper transfer function of all-pole and all-zero continuous-time fractional linear systems using one-dimensional digraphs theory D(1) has been presented. For the proposed method, an algorithm was constructed. The proposed solution allows minimal digraphs construction for any one-dimensional fractional system. The proposed method was discussed and illustrated with numerical examples.