This paper proposes an analytical method for the characterization of the set of all initial tumor and normal states of a cancer dynamical model for which there exists a successful drug administration therapy. The dynamical model considered simulates the behavior of the tumor and the normal cells populations growth in presence of a chemotherapy drug. This model is assumed to be affected by a state proportional uncertainty. The successful drug administration therapy is attained by respecting the tumor eradication and avoiding the lower admissible bound of the normal cells population which is viewed as an indicator of the patients health. The problem is posed in terms of domain of attraction computation and is solved by applying set theory and invariance tools.