This paper studies the problem of estimating the domain of attraction for delta operator systems under a pre-designed saturated linear feedback. Ellipsoids are used as the estimates of domain of attraction for delta operator systems. A condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractive invariant. Moreover, some necessary and sufficient conditions are given for single input delta operator systems. The results are also further extended to determine the invariant sets for delta operator systems with persistent disturbances. Linear matrix inequalities based on the methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements. Some numerical examples are given to illustrate the effectiveness of the developed techniques.