Geometric computation of value set boundaries

In this paper a general algorithm to find the boundaries of value sets bounded by elliptic arcs is developed. This algorithm uses a generalized line-sweep search procedure to extract the value set boundary from a set of generalized polygons describing the image of the bounding set or the extremal segments of the plant. The advantage of this approach is that, when the uncertainty is affine, it preserves the geometric parametrizations of value set boundaries. The effectiveness of this procedure is illustrated in the computation of value sets of affine uncertain plants.