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

Uncertain multiinput multioutput systems described in the frequency domain are discussed. The theory of nonnegative matrices and M-matrices is used along with majorant bounding techniques to develop robust stability and performance results for two types of uncertainty. The first type is uncertainty with norm-bounded subblocks. The second type is uncertainty that has subblocks with known patterns but unknown gains. This latter uncertainty representation allows the elements of a given uncertainty block to be correlated. For uncertainties of this type a recursive analysis methodology is developed which yields increasingly nonconservative results. Throughout this paper the performance analysis determines norm bounds on the deviations of the outputs from their nominal values. The results are illustrated by a numerical example