Open AccessDerivation and reduction of the singular Fornasini–Marchesini state‐space model for a class of multidimensional systems
Author(s) -
Zhao Dongdong,
Galkowski Krzysztof,
Sulikowski Bartlomiej,
Xu Li
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.0543
Subject(s) - realisation , eigenvalues and eigenvectors , mathematics , reduction (mathematics) , state space , state space representation , transfer function , class (philosophy) , state (computer science) , space (punctuation) , singular value , mimo , control theory (sociology) , pure mathematics , topology (electrical circuits) , algorithm , computer science , combinatorics , artificial intelligence , geometry , physics , engineering , statistics , control (management) , quantum mechanics , electrical engineering , operating system , beamforming
This study is devoted to derive the singular Fornasini–Machesini (F‐M) state‐space model for a class of MIMO multidimensional ( n ‐D) systems represented by non‐causal multivariate transfer function matrices. It is shown, first, that the singular n ‐D F‐M realisation can be generated by using the realisation methods of the standard n ‐D F‐M models. Since the resulted realisations are usually non‐minimal and deriving a minimal realisation is an extremely difficult problem, a model‐order reduction method is developed. In particular, the common eigenvector approach is proposed, which significantly reveals the relationship among the reducibility, the eigenvalues and the eigenvectors associated with a given singular F‐M state‐space model. An example of spatially interconnected, hexagonal circuit is also given to illustrate some details and confirm the effectiveness of the proposed method.