Ad-rank condition for controllability of linear control system on solvable Lie groups

TL;DR

This paper explores the controllability of linear control systems on solvable Lie groups, establishing that the ad-rank condition is sufficient for controllability in this context.

Contribution

It introduces the ad-rank condition as a criterion for controllability of linear systems on solvable Lie groups, extending classical results from Euclidean spaces.

Findings

ad-rank condition guarantees controllability on solvable Lie groups

generalizes controllability criteria from Euclidean spaces to Lie groups

provides a theoretical foundation for control design on Lie groups

Abstract

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. When the state space is a solvable connected Lie group, controllability of the linear system is assured if the ad-rank condition holds.