  This paper examines impulsive non-autonomous systems with grazing periodic
solutions. Surfaces of discontinuity and impact functions of the systems are
not depending on the time variable. That is, we can say that the impact
conditions are stationary, and this makes necessity to study the problem in a
new way. The models play exceptionally important role in mechanics and
electronics. A concise review on the sufficient conditions for the new type of
linearization is presented. The existence and stability of periodic solutions
are considered under the circumstance of the regular perturbation. To visualize
the theoretical results, mechanical examples are presented.
