Observability of linear systems on the Heisenberg Lie group

Fuente: arXiv
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Main Authors: Cavalheiro, Thiago Matheus, Santana, Alexandre José, Ayala, Victor
Format: Preprint
Published: 2025
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author Cavalheiro, Thiago Matheus
Santana, Alexandre José
Ayala, Victor
author_facet Cavalheiro, Thiago Matheus
Santana, Alexandre José
Ayala, Victor
contents In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time, even when direct measurements are impossible. By harnessing observability, we can accurately estimate the complete state of a system and reconstruct its dynamics using just limited information. In this work, we will find conditions for observability of linear systems in the three dimensional Heisenberg group $\mathcal{H}$. Considering the homomorphisms between the group and its simply connected subgroups, whose kernel is denoted by $K$, we will find sufficient conditions for observability on the system using a quotient space $\mathcal{H}/K$ as the output.
format Preprint
id arxiv_https___arxiv_org_abs_2503_19890
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Observability of linear systems on the Heisenberg Lie group
Cavalheiro, Thiago Matheus
Santana, Alexandre José
Ayala, Victor
Optimization and Control
In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time, even when direct measurements are impossible. By harnessing observability, we can accurately estimate the complete state of a system and reconstruct its dynamics using just limited information. In this work, we will find conditions for observability of linear systems in the three dimensional Heisenberg group $\mathcal{H}$. Considering the homomorphisms between the group and its simply connected subgroups, whose kernel is denoted by $K$, we will find sufficient conditions for observability on the system using a quotient space $\mathcal{H}/K$ as the output.
title Observability of linear systems on the Heisenberg Lie group
topic Optimization and Control
url https://arxiv.org/abs/2503.19890