Perturbed Markov chains are popular models for description of information networks. In such models, the transition matrix P0${\mathbf{P}}_0$ of an information Markov chain is usually approximated by matrix Pε=(1−ε)P0+εD${\mathbf{P}}_{\epsilon }=(1-\epsilon ){\mathbf{P}}_0+\epsilon \mathbf{D}$, where D$D$ is a so-called damping stochastic matrix with identical rows and all positive elements, while ε∈[0,1$\epsilon \in [0,1$] is a damping (perturbation) parameter. We perform a detailed perturbation analysis for stationary distributions of such Markov chains, in particular get effective explicit series representations for the corresponding stationary distributions π¯ε${\overline{\pi }}_{\epsilon }$, upper bounds for the deviation |π¯ε−π¯0|$|{\overline{\pi }}_{\epsilon }-{\overline{\pi }}_0|$, and asymptotic expansions for π¯ε${\overline{\pi }}_{\epsilon }$ with respect to the perturbation parameter ε$\epsilon$.