Lie algebra rank condition for bilinear control systems on $\mathbb{R}^2$

TL;DR

This paper characterizes the Lie algebra rank condition for controllability of bilinear control systems on the plane, providing new criteria and elementary techniques for analyzing the system's controllability.

Contribution

It offers a novel characterization of the Lie algebra rank condition specific to bilinear systems on  and introduces elementary methods to determine controllability.

Findings

Lie algebra rank condition characterized for  bilinear systems

Controllability criteria established for the system

Elementary techniques used to analyze the induced angular system

Abstract

We will study the controllability problem of a bilinear control system on $\mathbb{R}^2:$ the main result is the characterization of the Lie algebra rank condition for the system. On the other hand, using elementary techniques, we recover conditions for the controllability of the induced angular system on the projective space. Finally, we will give controllability criteria for the system.