Causality invariance of general systems under output feedback transformations

The causality preservation property (CPP) under output feedback transformations, a kind of closedness of causality under the transformations, is introduced as one of the basic system properties about a well-behaved system model. The causality of this paper is the one formulated as past-determinancy in the framework of the mathematical general systems theory. The paper presents a necessary and sufficient condition for a general time system to possess the CPP under the output feedback transformations, and demonstrates the significance of the result by identifying the essential condition which makes a class of linear systems well-posed under the transformations. The paper also discusses the relationship between the feedback transformations and the system inverse transformation, the transformation by interchanging inputs and outputs of a given system. This is of real conceptual significance because it gives a new insight into the feedback transformation. Introducing the auxiliary systems which will be termed (dual) associate systems, it is proved that some invariant properties of a system under the output feedback transformations are equivalent to those of the associate systems under the system inverse transformation. This result leads us to a new approach for the analysis of feedback systems.