On the characterization of the controllability property for linear control systems on nonnilpotent, solvable three-dimensional Lie groups

TL;DR

This paper provides a complete characterization of controllability for linear control systems on three-dimensional solvable nonnilpotent Lie groups using the Lie algebra rank condition and eigenvalue analysis.

Contribution

It introduces a method to determine controllability based on the LARC and eigenvalues of the derivation associated with the system's drift.

Findings

Controllability characterized by LARC and eigenvalues

Applicable to three-dimensional solvable nonnilpotent Lie groups

Simplifies controllability analysis for these systems

Abstract

In this paper we show that a complete characterization of the controllability property for linear control system on three-dimensional solvable nonnilpotent Lie groups is possible by the LARC and the knowledge of the eigenvalues of the derivation associated with the drift of the system.