  We present an exact master equation for a central spin-$1/2$ system coupled
to a spin-$1/2$ bath in terms of hyperfine interaction, which provides a
unified formalism for both free evolution and controlled dynamics of the
central spin. The equation enables us to study controllability of dynamics
processes with various degrees of non-Markovianity. We investigate the
Overhauser's effect on decoherence dynamics of the central spin under different
bath spectra and the system-bath coupling strengths. Nonperturbative leakage
elimination approach is applied to the system to suppress decoherence in
solid-state quantum information processing.
