The stability robustness of discrete linear time-invariant systems in state-space models is analysed. Based on a root-locus approach and from the stable-eigenvalue viewpoint, fundamental criteria for testing the stability robustness of autonomous systems are derived and applied to the robustness analysis of multivariable feedback systems. Both the norm bound and the element bounds for the allowed perturbations are obtained. A stability robustness index is denned which is useful both for the analysis and synthesis of control systems.