Abstract
As a well-known result in the linear system theory, the controllable pairs {A, b} of a system described by dx/dt=Ax+bu, exist generically. This paper considers an analogy in the case of systems on compact Lie groups. It is proved that the same result also holds, if systems are defined on compact semi-simple Lie groups, and the both conditions, compact and semi-simple, are essential. The proof is mainly supported by the root system theory of compact semisimple Lie algebras, so it does not depend on the representative form of a Lie algebra. The result will give a good insight to recognize the system classes which have the same important property as the linear systems.
