KW-models for (multivariate) linear differential systems

TL;DR

This paper introduces KW-models, a class of state models for linear differential systems, establishing a one-to-one correspondence between these systems and minimal proper KW-models, thus advancing the understanding of their state representations.

Contribution

The paper defines KW-models and proves a canonical correspondence between linear differential systems and minimal proper KW-models, offering a new framework for their analysis.

Findings

Establishment of a one-to-one correspondence between systems and KW-models

Introduction of a canonical form for linear differential systems

Advancement in state representation theory for differential systems

Abstract

A class of state models, called Kronecker-Weierstrass models (or, simply, KW-models), is introduced, and the state representation problem for linear differential systems is studied in the context of these models. It is shown, in particular, that there is a canonical one-to-one correspondence between linear differential systems and similarity classes of minimal proper KW-models.