Noncommutative rational functions, their difference-differential calculus and realizations

TL;DR

This paper surveys noncommutative rational functions, their realization theory, and applications, while introducing a difference-differential calculus as a new analytical tool in system theory and control.

Contribution

It provides a comprehensive overview of noncommutative rational functions and develops a novel difference-differential calculus for their analysis.

Findings

Unified framework for noncommutative rational functions

Development of difference-differential calculus

Applications in system theory and control

Abstract

Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions, their realization theory and some of their applications. We also develop a difference-differential calculus as a tool for further analysis.