Linear systems, and ARMA- and Fliess models

Abstract

Linear (dynamical) systems are central objects of study (in linear system theory), and ARMA- and Fliess models are two very important classes of models that are used to represent them. This article is concerned with the question of what is a relation between them (in case of higher dimensions). It is shown that the category of linear systems, the ‘weak’ category of ARMA-models and the category of Fliess models are equivalent to each other.

Keywords:

• behaviour
• linear system
• ARMA-model
• Fliess model
• weak equivalence
• stable isomorphism