A method of control feedback design for systems with hereditary properties is presented which is based on the concept of anisochronic state space. A new kind of state feedback control is proposed using as state variables the system accumulation attributes only, while the other delay dynamics are represented by functional terms. Assigning the control parameters is approached as a placement of characteristic function zeros; however, owing to the infinite set of these zeros in the hereditary system, only the dominant zeros are placed. For this purpose a new technique applying the conformal mapping of transcendental characteristic function of the hereditary system has been developed.