The article describes the task of the stabilization of the inverted pendulum on the rotating platform in the upmost position based on linear model with respect to small deviations. Working with real devices is always a source of the delay in the control channel which in particular circumstances leads to the loss of stability of the closed loop system. The proposed solution is based on the continuous pole placement method. The main complication of the delay systems stabilization is the infinite number of the poles. Suggested method is based on transition from considering the infinite dimensional system to moving only finite number of the rightmost roots to the left half-plane by applying small changes to the feedback coefficients vector. Changes are calculated by finding sensitivities of roots with respect to small variations of the feedback vector (in fact, partial derivatives). The main advantage of the method is simplicity of the realization of the synthesized feedback on the plant's board controller. Results of the computer modelling are given, efficiency of the described method is demonstrated with particular value of the delay.