An M-matrix and majorant approach to robust stability and performance analysis for systems with structured uncertainty

The authors use the theory of nonnegative and M-matrices to develop robust stability and performance results for two types of uncertainty characterizations. Performance is measured in terms of the deviations of the system outputs from their nominal values. For uncertainty with norm-bounded subblocks the development leads to a frequency-dependent multiloop small-gain theorem. The stability result is shown to be necessary and sufficient when the nominal transfer matrix is block-diagonal. For uncertainty that has subblocks with known patterns the developments lead to a recursive methodology which is guaranteed to yield increasingly nonconservative results