Abstract
In this paper we introduce the concept of a basic linear system which is defined as a strongly stationary, output complete and strongly precausal time system with a finite dimensional system core, and investigate some properties of it. The concept is shown an axiomatized model of constant coefficient linear ordinary differential equation systems.
The main results of this paper are:
i) A reduced state space representation of a basic linear system is shown to be unique up to isomorphism. This implies an interesting fact that basic linear systems form a class of time systems whose state space representations are not arbitrary.
ii) As an application of i) controllability and stability properties are investigated in relation to system behaviors. As for controllability a controllability condition of a basic linear system is described in the term of the input output relation. As for stability we intoroduce the concept of output stability as a stability concept concerning system behaviors and show that the output stability implies and is implied by the traditional state space stability for a basic linear system.
The above considerations lead us to the conclusion that the concept of basic linear systems is, although general and fairly abstract, structured richly enough to produce interesting results and that it can be fundamental conceptual framework for linear systems theory.
