  A formalism based on Pontryagin's maximum principle is applied to determine
the time-optimal protocol that drives a general initial state to a target state
by a Hamiltonian with limited control, i.e., there is a single control field
with bounded amplitude. The coupling between the bath and the qubit is modeled
by a Lindblad master equation. Dissipation typically drives the system to the
maximally mixed state; consequently, there generally exists an optimal
evolution time beyond which the decoherence prevents the system from getting
closer to the target state. For some specific dissipation channel, however, the
optimal control can keep the system from the maximum entropy state for
infinitely long. The conditions under which this specific situation arises are
discussed in detail. The numerical procedure to construct the time-optimal
protocol is described. In particular, the formalism adopted here can
efficiently evaluate the time-dependent singular control which turns out to be
crucial in controlling either an isolated or a dissipative qubit.
