Abstract
In this paper, the relative stability of control systems with uncertainty is studied. It is shown that relative stability problems such as the degree of stability and stability margin are reduced to the evaluation of the image of characteristic function under perturbation of parameters. To get an approximation of the image, the addition and multiplication of intervals is used. As intervals in the complex plane, the family of polygons are used, and traditional interval analysis in the real line is generalized to the complex plane. Moreover, to get a good approximation of the image, 2 methods are used: one is the method based on the decomposition of extreme points of convex polygons, and the other is the method based on the partition of polygons. The former method includes the method based on the mapping theorem as a special case.
