System embedding: arbitrary images (Q1881974)

The aim of this paper is to use quotient algebra to develop a new approach of system embedding to analysis and synthesis of linear systems. A model is reduced via a regularizing supplement to a special nonsingular matrix, called promatrix, and then the system embedding is realized by means of the inverse of the promatrix and of an associated square rational matrix, called the image of the system. Necessary and sufficient conditions are given for embeddability of a system represented by a promatrix. The concepts of constructive and integral embeddings are discussed and necessary and sufficient conditions for a system to be constructively embeddable are obtained via matrix factorizations. It is emphasized that the general embedding conditions presuppose an arbitrary supplement of the uncontrollable and unobservable parts of the system.