A unification of system equivalence definitions

The concept of system equivalence was introduced by Rosenbrock to generalize the notion of system similarity to nonstate-space models, i.e., to systems described by polynomial operators. The idea of equivalence is relatively natural: given two descriptions of the same physical system by two different observers, we would like to assert whether these descriptions are the same from a "coordinate-free" point of view. In this paper, system equivalence is studied from both the polynomial and the state-space points of view. Previous definitions of system equivalence are connected together, and an alternative definition is proposed. This new approach is based on constructing complete information sets for a given differential system by expanding its usual input/ output map. This idea generalizes the earlier concept of maximal-strict system equivalence introduced by Morf.