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Robustness of uncertain MIMO systems-an overview and a new perspective

The critical direction theory is proposed as a new tool for analyzing the robustness of uncertain systems. The analysis is done using Nyquist arguments involving eigenvalues instead of singular values, and yields exact necessary and sufficient conditions for robust stability. The concept of a critical line on the Nyquist plane is defined and used to calculate the Nyquist robust stability margin. The new approach gives alternatives to computing exact stability margins in some cases of highly directional uncertainty templates where other methods are not applicable. An overview of major robust stability results reported in the literature is given for the purpose of comparison with the perspective of the new paradigm.