Algebraic Analysis Applied to the Theory of Linear Dynamical Systems
This work provides a foundational reformulation for researchers in control theory and dynamical systems, but it is largely conceptual and incremental.
The paper redefines the modern theory of linear dynamical systems by adapting concepts from algebraic analysis, specifically Grothendieck's algebraic geometry, to unify and formalize the framework developed by Fliess, Willems, Oberst, and others.
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.