Remarks on the formulation of model order estimation

The model order determination for linear time-invariant systems from measured input-output signals is essential for defining the right structure of a real process. The purpose of this paper is to note some concepts regarding the order determination, approaching the problem from an empirical point of view. At first the generalization to an uncertain measurement set of a simple criterion for order estimation is proposed. Then some ideas, that lead to the model order determination, are reviewed using the concept of rank degeneracy of a matrix. Finally a combined procedure for minimum order selection is outlined referring to the concepts of balanced representation for discrete time-invariant linear systems.