For a control system on the sphere with two skew-symmetric matrices A and B, the nonzero bracket condition [A,B]≠0 guarantees controllability, and the paper constructs the steering trajectories explicitly.
Lie algebra rank condition for bilinear control systems on $\mathbb{R}^2$
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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.
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Controllability of induced bilinear systems on the sphere
For a control system on the sphere with two skew-symmetric matrices A and B, the nonzero bracket condition [A,B]≠0 guarantees controllability, and the paper constructs the steering trajectories explicitly.