Modeling of multidimensional linear systems

Abstract

This thesis deals with modeling and classification of multidimensional linear systems. In a behavioural framework, two representations of such systems are used: AR representations and ARMA representations. Three first-degree ARMA representations: Dual Pencil, Pencil, and Descriptor representations are defined and recasting methods between them are given. Several rank conditions which allow these recasting methods to result in equivalent representations with fewer auxiliary variables are found. With respect to each first-degree model a definition of order is given and some necessary rank conditions which allow reduction of order are derived. All AR representations of a given behaviour are associated with a vector space generated by their row spaces. A definition of order for each AR representation associated with this vector space is given and it is shown how to obtain a minimal order AR representation from any given AR representation using primary decomposition of polynomial equations and their p-adic valuations. A survey of the existing work that shows its limitations and extent is given.