The design of feedback systems based on a 'mathematical model' of the plant should be insensitive to uncertainty associated with the parameters of the model. This is required since the system model parameters, in most cases, are only a best estimate of the real plant. The concepts of gain and phase margins evolved to guarantee closed-loop stability in the presence of specified uncertainty of the plant gain/phase characteristics. Thus, the design of 'robust' feedback systems has been extensively studied in the control literature. In the multivariable control setting, a wide range of robustness metrics has been postulated to character ise system behaviour under plant ignorance. The nature of the feedback design technique also influences the selection of appropriate robustness criteria, and this is also true for eigenstructure assignment. During the characterisation of eigenstructure assignment using state and output feedback, it was emphasised that for the solution to exist, the eigenvector matrix (X) must be non-singular. In this chapter this non-singularity of X will be numerically quantified and its relationship to the robustness of the resulting solution will be explained.