Given a nominally regular, impulse-free and D-stable linear singular system, a one-parameter family of perturbations is considered. Several new formulas related to the Kronecker operations of linear fractional transformations (LFTs) are established. Based on LFT technique and guardian map theory, a systematic approach is provided to derive a closed-form solution for the maximal bounds under which the regularity, impulse immunity and D-stability are preserved to achieve required performance and robust stability. The LFT approach provides a uniform framework for robustness analysis, for both uncertain linear continuous-time and discrete-time singular systems. Two examples are given to illustrate the approach.