Controllability of invariant systems on lie groups and homogeneous spaces

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Controllability of linear systems on lie groups (2011, background): “In the case where G is simply connected, it is di eomorphic to G̃ and ΣF cannot be controllable: it is indeed a right invariant system whose vector elds are contained in a half-space bounded by the Lie subalgebra L0 (Hypersurface Principle, Cf [14]).”
Time minimal trajectories for a spin 1∕2 particle in a magnetic field (2005, unknown): “For these kinds of systems very powerful techniques were developed both for what concerns controllability [21, 23, 26, 32] and optimal control [3, 12, 25].”
Control theory on lie groups (2009, background): “The bibliography contains references of several kinds: (1) textbooks on control theory [1, 14, 30], sub-Riemannian geometry [28], nonholonomic dynamics [48], and differential geometry and Lie groups [49], (2) works on controllability of invariant systems on Lie groups [2–5, 11–13, 15–17, 19, 21, 22,”
Controllability properties for finite dimensional quantum Markovian master equations (2002, methodology): “The infinitesimal structure of the so-called quantum Markovian master equation, i.e. the “axiomatic” model for an open quantum system, is known since the works of Lindblad [14] and Gorini-KossakowskiSudarshan [7] and it is a prerequisite for the utilization of the Lie algebraic controllability…”