The invariance problem is considered in the paper for linear stationary systems with relay control inputs. The classical way of solving this problem is using sliding mode control algorithms. When actuators have the imperfections, the chattering problem exists. In this paper the invariance problem is considered for systems with non-ideal relay actuators. The proposed approach consists in using high frequency modulation signal to linearize the switching characteristics of relays. Then dynamic compensator approach is utilized for averaged system. The simulation results show the efficiency of the proposed algorithms.