Robust stability with multilinear perturbations: how good is the convex hull approximation?

A computer-aided design technique is presented to study robust stability of a feedback system which includes bounded perturbations entering affine multilinearly into the coefficients of the plant. This computer-aided technique allows for the graphical construction of the convex hull approximation of the so-called value set. Generating the `true´ value set by gridding the perturbations rectangle, the goodness of the approximation is checked. This comparison was performed studying a number of real world examples subject to perturbations recently introduced in the literature on robustness, including RCL circuits, DC motors and the model of a supersonic transport plane. In all the real world examples examined, a tight convex hull approximation was always obtained