  In this letter, we apply optimal control theory to design minimum-energy
$\pi/2$ and $\pi$ pulses for the Bloch system in the presence of relaxation
with constrained control amplitude. We consider a commonly encountered case in
which the transverse relaxation rate is much larger than the longitudinal one
so that the latter can be neglected. Using the Pontryagin's Maximum Principle,
we derive optimal feedback laws which are characterized by the number of
switches, depending on the control bound and the coordinates of the desired
final state.
