Formal Definitions and General Properties

Abstract

In this section, we introduce formally the concept of an input-output linear system. Like the state space systems of Part II, input-output systems serve as models for real-world processes which may be viewed as “boxes” which take input functions to output functions in some linear manner. The differences between input-output linear systems and state space linear systems, however, are both philosophical and substantial. Processes which are modeled appropriately with state space linear systems have associated with them some notion of an internal situation whose initial setting might influence the outcome of an input-output “experiment” on the process. On the other hand, input-output linear systems may be used as models for processes having associated with them no well-defined concept of what constitutes an internal situation; the only experiments one may perform on such a black box-type process are of the input-output variety. Proceeding in the spirit of §6, we propose the following definitions.