The authors give a number of necessary and sufficient conditions for robust stability of linear time-invariant uncertain systems which exploit the concept of well-posedness of feedback systems understood in the sense defined in [M. A. Dahleh and I. J. Diaz-Bobilio, Control of uncertain systems. A linear programming approach. Prentice Hall (1995; Zbl 0838.93007)] for example. (By the way it seems rather strange that this monograph [Dahleh and Diaz (loc. cit.)] is not cited in the paper although there exist many common points in the presented results.) The conditions for well-posedness and in turn for robust stability are represented by matrix inequalities in Hermitian forms. Small gain type conditions are given using linear fractional transformations and the links between frequency domain \(H_\infty\) conditions and the state-space setting based on parameter dependent Lyapunov functions are presented. The authors compare their results with the structured singular value approach [e.g., K. Zhou, J. Doyle and K. Glover, Robust and optimal control. Prentice Hall (1996)] and the integral quadratic constraint condition [e.g., A. Magretski and A. Rantzer, IEEE Trans. Autom. Control 42, No. 6, 819-830 (1997; Zbl 0881.93062)]. They present examples indicating that the conditions given in the paper are less conservative due to the concept of vertex-separator introduced to generalize the \(D\)-scaling.