Method for Finding a set of (A,B,C,D) Realizations for Single-Input Multiple-Output / Multiple-Input Single-Output One-dimensional Continuous-time Fractional Systems - Markowski, Konrad Andrzej; Hryniów, Krzysztof (Journal of Applied Nonlinear Dynamics, 2026)
In the paper presented is a method allowing for determination of a set of (A,B,C,D) realizations for fractional-order dynamic systems. Proposed method is an extension of previously proposed algorithm that was used to determine realizations of fractional-order 1D single-input single-output (SISO) dynamic systems for both single-input multipleoutput (SIMO) and multiple-input single-output (MISO) fractional dynamic systems. The main advantage of the method over canonical forms is that the algorithm finds a set of realizations, not just a single realization. Also, the solutions found tend to be minimal in terms of size of state matrix A. Additionally, the method allows for the possibility of obtaining a set of state matrices directly from digraph form of the system and can be efficiently used as GPGPU computer algorithm. Proposed method is presented in pseudo-code and illustrated with example.