In this paper, we propose a simple approach to analyse stability robustness of discrete-time singular systems under structured perturbations. The developed robustness criteria are then applied to solve robust regional pole-assignment problems of singular systems. A robust control design algorithm, via state feedback, is also given. The robust stability problem of singular systems is more complicated than that of regular systems. Not only stability robustness but system regularity and impulse elimination should be considered simultaneously. Since the results of robust control and analysis for singular systems is not available in the literature as much as other fields, the paper may be viewed as a complementary result in this field. Although only discrete-time case is discussed, several results can be directly applied to continuous-time systems as well.