The present analysis deals with the regularity of solutions of bilinear
control systems of the type x′=(A+u(t)B)xwhere the state x belongs to some
complex infinite dimensional Hilbert space, the (possibly unbounded) linear
operators A and B are skew-adjoint and the control u is a real valued
function. Such systems arise, for instance, in quantum control with the
bilinear Schr\"{o}dinger equation. For the sake of the regularity analysis, we
consider a more general framework where A and B are generators of
contraction semi-groups.Under some hypotheses on the commutator of the
operators A and B, it is possible to extend the definition of solution for
controls in the set of Radon measures to obtain precise a priori energy
estimates on the solutions, leading to a natural extension of the celebrated
noncontrollability result of Ball, Marsden, and Slemrod in 1982. Complementary
material to this analysis can be found in [hal-01537743v1