Control sets of linear systems on Lie groups

TL;DR

This paper investigates the properties of maximal approximate controllability sets for linear systems defined on Lie groups, extending classical control theory from Euclidean spaces to more general geometric structures.

Contribution

It introduces a study of controllability sets for linear systems on Lie groups, a novel generalization beyond traditional Euclidean space analysis.

Findings

Characterization of maximal controllability sets on Lie groups

Extension of controllability concepts to non-Euclidean geometries

Foundations for control design on Lie groups

Abstract

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.