  We study the dissipative dynamics of a qubit that is afflicted by classical
random telegraph noise and it is subject to dynamical decoupling. We derive
exact formulas for the qubit dynamics at arbitrary working points in the limit
of infinitely strong control pulses (bang-bang control) and we investigate in
great detail the efficiency of the dynamical decoupling techniques both for
Gaussian and non-Gaussian (slow) noise at qubit pure dephasing and at optimal
point. We demonstrate that control sequences can be successfully implemented as
diagnostic tools to infer spectral proprieties of a few fluctuators interacting
with the qubit. The analysis is extended in order to include the effect of
noise in the pulses and we give upper bounds on the noise levels that can be
tolerated in the pulses while still achieving efficient dynamical decoupling
performance.
