2134/36004
Iman M.O. El-Nabrawy
Algebraic issues in linear multi-dimensional system theory
2018
Loughborough University
untagged
2018-11-15 15:26:03
article
https://repository.lboro.ac.uk/articles/Algebraic_issues_in_linear_multi-dimensional_system_theory/9374321
1-D Multivariable system theory has been developed richly over the past
fifty years using various approaches. The classical approach includes the matrix
fraction description (MFD), the state-space approach etc., while the behavioural
approach is relatively new. Nowadays, however there is an enormous
need to develop this theory for systems where information depends on more
than one independent variable i.e. the n-D system theory (n ≥ 2), due to
the vast number of applications for these kind of systems. By contrast to the
1-D system theory, the n-D system theory is less developed and its main aspects
are not yet complete, where generalising the results from 1-D to n-D has
proved to be not straight forward nor smooth. This could be attributed to the
n-D polynomial matrices which are the basic elements used in the analysis of
n-D systems. n-D polynomial matrices are more difficult to manipulate when
compared to the 1-D polynomial matrices used in the analysis of 1-D systems,
because the ring of n-D polynomials to which their elements belong does not
possess many of the favourable properties which the ring of 1-D polynomials
possesses. The work proposed in this thesis considers the Rosenbrock system
matrix and the matrix fraction description approaches to the study of n-D
systems. [Continues.]