Lie algebra rank condition for bilinear control systems on ℝ²

2025/06/03 by Cruz-Mullisaca, Efrain, Patty-Yujra, Victor H.
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2506.02428

Abstract

We will study the controllability problem of a bilinear control system on ℝ²: 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.

Related

• Controllability of induced bilinear systems on the sphere
• Combinatorics-Based Approaches to Controllability Characterization for Bilinear Systems
• The Lie Algebra Rank Condition for Non-Bilinear Quantum System
• Ad-rank condition for controllability of linear control system on solvable Lie groups
• Bilinear Systems Induced by Proper Lie Group Actions