The paper proposes a unified approach to the asymptotic analysis of a Markov decision process (MDP) with an \(\varepsilon\)-additive perturbation irrespective of whether the perturbation is regular or singular. It shows that an optimal solution to the perturbed MDP can be approximated by an optimal solution of the limit Markov control problem for sufficiently small perturbations. Investigating the discounted case it is shown that an optimal solution to the perturbed MDP can be approximated by an optimal solution of the original MDP for sufficiently small perturbations. The same conclusion can be derived for the unichain, the communicating and the discounted cases.