Polynomial matrix equivalences: system transformations and structural invariants

The present article is a survey on linear multivariable systems equivalences. We attempt a review of the most significant forms of system equivalence having as a starting point matrix transformations preserving certain aspects of their spectral structure. From a system theoretic point of view, the need for a variety of forms of polynomial matrix equivalences, arises from the fact that different types of spectral invariants give rise to different types of dynamics of the underlying linear system. A historical perspective of the key results and their contributors is also given.

Automated summary

This article provides a survey on linear multivariable systems equivalences, focusing on matrix transformations preserving certain aspects of their spectral structure. It discusses the need for various forms of polynomial matrix equivalences due to different types of spectral invariants giving rise to different dynamics of the underlying linear system. Additionally, a historical perspective of key results and contributors is presented.