Algebraic Analysis Applied to the Theory of Linear Dynamical Systems

TL;DR

This paper explores the application of algebraic analysis, rooted in algebraic geometry, to the modern theory of linear dynamical systems, highlighting its theoretical foundations and potential for solving analytic problems.

Contribution

It provides a modern algebraic framework for linear dynamical systems inspired by algebraic analysis and algebraic geometry.

Findings

Establishes a connection between algebraic analysis and linear dynamical systems

Provides a new algebraic perspective on solving analytic problems in system theory

Highlights the influence of Grothendieck's EGA on system analysis methods

Abstract

The expression "Algebraic Analysis" was coined by Mikio Sato. It consists of using algebraic notions to solve analytic problem. The origin of Algebraic Analysis is Algebraic Geometry as was developed by Alexander Grothendieck and his school. Mimicking the introduction of Grothendieck's EGA (changing only a few words) one obtains a good definition of the modern theory of linear dynamical systems, as developed by Michel Fliess, Ian Willems, Ulrich Oberst and others.