Controllability of right invariant systems on real simple Lie groups (Q801858)

Let G be a Lie group with Lie algebra L and let \(\Gamma =\{A+uB\), \(u\in {\mathbb{R}}\}\) be a family of right invariant vector fields on G. \(\Gamma\) is strongly controllable if the elements of the form exp(tX) with \(t\geq 0\) and \(X\in \Gamma\) generate G. Moreover, \(\Gamma\) satisfies the rank condition when A and B generate L. The authors identify five types of Lie groups and a set of (open) conditions on \(\Gamma\) such that strong controllability is equivalent to the rank condition.