A digraph approach to the state-space model realization of MIMO non-commensurate fractional order systems

This paper proposes a novel approach that can generate a state-space model with low inner dimension for an MIMO non-commensurate fractional order (NCFO) system. Specifically, the notion of an admissible digraph is firstly introduced associated with a fractional order transfer (function column) vector. Then, new state-space model realization conditions and corresponding procedures based on this admissible digraph are proposed for the state-space model realization of an NCFO polynomial transfer matrix. Finally, a new necessary and sufficient state-space model realization condition is proposed for the rational transfer matrix of an MIMO NCFO system, and it is shown, based on a matrix fractional description (MFD) of the given rational transfer matrix, a state-space model realization can be obtained by firstly converting it to the polynomial case and then utilizing the digraph approach for polynomial case. Symbolic and numerical examples are provided to demonstrate the main ideas and effectiveness of the proposed digraph approach. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a novel approach to generate a state-space model with low inner dimension for an MIMO non-commensurate fractional order system. The concept of an admissible digraph associated with a fractional order transfer vector is introduced. New state-space model realization conditions and procedures based on this admissible digraph are proposed for the state-space model realization of an NCFO polynomial transfer matrix. A new necessary and sufficient state-space model realization condition is also proposed for the rational transfer matrix of an MIMO NCFO system.