Multi-dimensional (n-D) systems can be described by matrices whose elements
are polynomial in more than one indeterminate. These systems arise in the study
of partial differential equations and delay differential equations for example, and
have attracted great interest over recent years. Many of the available results have
been developed by generalising the corresponding results from the well known
1-D theory. However, this is not always the best approach since there are many
differences between 1-D, 2-D and n-D (n>2) polynomial matrices. This is due
mainly to the underlying polynomial ring structure. [Continues.]
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.
Engineering and Physical Sciences Research Council.