A note on two methods related to stability robustness of polynomials in a sector (relative stability)

Two recent results on the stability robustness of uncertain systems (polynomials) are addressed. One gives a vertex test for left-sector (relative) stability, where the number of the required vertices is four for a real case and eight for a complex case. The other gives an elegant frequency-domain graphical (hodograph) approach for left-plane stability, where the plotting of only one (two for a complex case) hodograph plus simple boundary conditions is both necessary and sufficient to obtain the maximum coefficient perturbation bounds. It is shown that a similar graphical test exists for the left-sector stability case