Some notes on valuation theory in linear systems

In recent years, there has been an increasing interest in the pole-zero structure of multivariable sytems, at both finite and infinite frequencies. However, in most present approaches there is a certain asymmetry (which we shall elaborate below) in the treatment of the finite and infinite points. In this paper, we shall indicate how the language of valuation theory can be used to give a more uniform treatment of finite and infinite frequencies and more generally of polynomial and rational matrices.