Abstract
It is important to find the system of minimal complexity among equivalent systems, that is, systems with the same input-output relation.
As for finite dimensional linear time-invariant systems, minimal complexity is considered as minimal dimension. The algorithm for obtaining irreducible realization is given. And the close relation between controllability, observability and irreducibility is presented.
As for linear time-invariant systems with delay, a few concepts of controllability are defined and necessary and sufficient conditions for them are given. Also the relation between controllability, observability and irreducibility is investigated.
This paper is concerned with time-invariant linear systems with delay. The number of integrators or the number of delay lines needed to construct the system is used to demonstrate the complexity of the system. Two irreducibilities, one for minimal integrator and one for minimal delay line, are considered, and an algorithm for obtaining systems with such properties is introduced. Two kinds of controllability and observability, ones for integrators and ones for delay lines, are defined, and the necessary and sufficient conditions for these properties are given. Close relations among these controllabilities, observabilities and irreducibilities mentioned above are presented.
