Abstract
This paper deals with affine invariant control systems on Lie groups. There is given a criterion for controllability of hypersurface invariant systems. For some subclass of simply connected solvable Lie groups G there is obtained a complete characterization of controllable multi-input affine systems on G. A lower bound of the number of controlled vector fields necessary to achieve controllability on simply connected Lie groups is given. Then the necessary conditions and sufficient conditions for controllability of single-input systems on solvable Lie groups are obtilined.
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