Robust analysis with respect to real parameter uncertainty

This paper revisits the problem of assessing robust stability of linear uncertain systems. It focus on systems with a single uncertain real parameter, in which case finite dimensional necessary and sufficient conditions for robust stability can be constructed in the form of LMIs (linear matrix inequalities). Among other things, we revisit and propose alternative LMI tests for a problem of computing the structured singular value with (D,G)-scalings and show that an existing condition for the existence of an affine parameter-dependent Lyapunov function which is known to be sufficient is also necessary in the case of a single uncertainty.