  We consider the problem of steering control for the systems of one spin 1/2
particle and two interacting homonuclear spin 1/2 particles in an
electro-magnetic field. The describing models are bilinear systems whose state
varies on the Lie group of special unitary matrices of dimensions two and four,
respectively. By performing decompositions of Lie groups, taking into account
the describing equations at hand, we derive control laws to steer the state of
the system to any desired final configuration. Explicit formulas are given for
the parameters involved in the control algorithms. Moreover, the proposed
algorithms allow for arbitrary bounds on the magnitude of the controls and for
some flexibility in the specification of the final time which must be greater
than a given value but otherwise arbitrary.

Quantum Physics