This paper is devoted to the study of behavior of open quantum systems consistently based on the Franke–Gorini–Kossakowski–Lindblad–Sudarshan (FGKLS) equation which covers evolution in situations when decoherence can be distinguished. We focus on the quantum measurement operation which is determined by final stationary states of an open system—so called pointers. We find pointers by applying the FGKLS equation to asymptotically constant density matrix. In seeking pointers, we have been able to propose a perturbative scheme of calculation, if we take the interaction components with an environment to be weak. Thus, the Lindblad operators can be used in some way as expansion parameters for perturbation theory. The scheme we propose is different for the cases of non-degenerate and degenerate Hamiltonian. We illustrate our scheme by particular examples of quantum harmonic oscillator with spin in external magnetic field. The efficiency of the perturbation algorithm is demonstrated by its comparison with the exact solution.