Unified approach to linear system theory

In this paper, a unified approach to linear system theory is presented. The abstract system models for both finite and infinite dimensional linear systems are defined over an operator space based on the operational algebra structure. Then the behavior of these systems can be studied in terms of abstract system models in a unified form within the same framework, and the concrete system properties can be obtained easily by associating the abstract model with concrete system models. There appears in this paper a few results obtained recently. Firstly, as brief mathematical preliminaries, the operators and operator space are introduced. The abstract system models defined over the operator space are then presented. Thirdly, the structural properties of the abstract models are investigated in detail. Finally, the conclusions and remarks are discussed shortly.