Grushin problems and control theory: Formulation and examples

TL;DR

This paper introduces a novel formulation of control problems using Grushin problems, providing clearer interpretations of controllability, observability, and stability in control theory.

Contribution

It presents a new approach to control theory by reformulating classical notions through Grushin problems, enhancing conceptual understanding.

Findings

Reformulation of controllability, observability, and stability using Grushin problems

Provides an easier interpretation of control concepts

Establishes a new framework for control problem analysis

Abstract

In this paper we give a new formulation of an abstract control problem in terms of a Grushin problem, so that we will reformulate all notions of controllability, observability and stability in a new form that gives readers an easy interpretation of these notions.