  We introduce the control conditions for 0th order pseudodifferential
operators $\mathbf{P}$ whose real parts satisfy the Morse--Smale dynamical
condition. We obtain microlocal control estimates under the control conditions.
As a result, we show that there are no singular profiles in the solution to the
evolution equation $(i\partial_t-\mathbf{P})u=f$ when $\mathbf{P}$ has a
damping term that satisfies the control condition and $f\in C^{\infty}$. This
is motivated by the study of a microlocal model for the damped internal waves.
