Linear control systems on the homogeneous spaces of the Heisenberg group

TL;DR

This paper classifies linear control systems on homogeneous spaces of the Heisenberg group and analyzes their control properties, focusing on a specific two-dimensional non-simply connected space.

Contribution

It provides a complete classification of linear control systems on homogeneous spaces of the Heisenberg group and studies their controllability and control sets.

Findings

Classified all linear control systems on homogeneous spaces of H

Analyzed controllability properties of a specific 2D non-simply connected space

Detailed study of control sets and dynamics on these spaces

Abstract

Let H denote the 3-dimensional Heisenberg Lie group. The present paper classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups and expose a detailed study on the control behavior (controllability property and control sets) of a particular dynamics evolving on a non simply connected homogeneous (state) space of dimension two.