It is demonstrated for the first time that the new criteria developed by Chang and Chen (1988), for a linear multivariable system to guarantee the stability of systems subjected to non–linear time–varying uncertainties, are not only sufficient but are also necessary ones. In addition, it is also shown that the previous results can be extended to a more simple and testable form which just contains the unstable part of the plant, to facilitate the analysis and synthesis of system robustness. An illustrative example confirms the availability of these new results.