  We show that dissipative quantum state preparation processes can be protected
against qubit dephasing by interlacing the state preparation control with
dynamical decoupling (DD) control consisting of a sequence of short
$\pi$-pulses. The inhomogeneous broadening can be suppressed to second order of
the pulse interval, and the protection efficiency is nearly independent of the
pulse sequence but determined by the average interval between pulses. The DD
protection is numerically tested and found to be efficient against
inhomogeneous dephasing on two exemplary dissipative state preparation schemes
that use collective pumping to realize many-body singlets and linear cluster
states respectively. Numerical simulation also shows that the state preparation
can be efficiently protected by $\pi$-pulses with completely random arrival
time. Our results make possible the application of these state preparation
schemes in inhomogeneously broadened systems. DD protection of state
preparation against dynamical noises is also discussed using the example of
Gaussian noise with a semiclasscial description.
