Abstract
In system theory, one of the most basic problems is to find a reduced form of a system, where the reduced form of the system is a system with minimum dimensional state space which is equivalent to the given system. As is well known, for usual linear systems this reduction problem is solved almost completely, and the concept of irreducibility is closely related to the concepts of controllability and observability.
This paper is concerned with the concept of irreducibility of linear stationary systems with time lag. The necessary and sufficient conditions for controllability and for observability are given in terms of the system parameters. A few concepts of irreducibillity are defined, and it is shown these concepts of irreducibility are closely related to the concepts of controllability and observability. For a type of irreducibility, an algorithm for determining the reduced form of the system is given.
