Basic linear systems and their categorical realization theory

In this paper the following problem is considered: Given an unstructured dynamical input-output model, i.e., a time system. If the systems properties like causality, stationarity, linearity, and the finiteness condition are imposed on the system, what will its resulting characteristics? This problem is investigated in order to define a meaningful subclass of time systems and to check whether or not the set of systems properties available from the present systems theory is complete enough to describe systems behavior fruitfully. The class of basic linear systems is introduced as the meaningful subclass of time systems, and their properties and representation theory are discussed in terms of category theory. This research implies that affirmative answers can be obtained for the completeness question.