Abstract
In this paper we considered a realization theory of general stationary linear dynamic systems and, based on the consideration, discussed a characterization of constant coefficient linear ordinary differential equation systems in the framework of general systems theory.
We showed that a necessary and sufficient condition for an input-output response family to be realizable is that the family satisfy two properties, namely, input response consistency and state response consistency, and that the input response consistency, stationarity, strong causality and finite dimensionality can essentially characterize the differential equation systems.
Since we treat general linear systems, the realization problem of this paper is different from the conventional one. However, we demonstrated that our general result implies the ordinary one if the systems in consideration are restricted to the class of differential equation systems.
In conclusion we pointed out and demonstrated that our general treatment of linear systems leads to the construction of an axiomatic linear system theory, which will be discussed in a subsequent paper.
