Application of value set concept to ellipsoidal polynomial families with multilinear uncertainty structure

Abstract

The contribution intends to present the application of the value set concept to the ellipsoidal polynomial families with multilinear uncertainty structure. It is a follow-up to the previously published work, where the ellipsoidal polynomial families with affine linear uncertainty structure were studied. In the first parts of this paper, the basic terms related to the robustness under parametric uncertainty (e.g., uncertainty structure, uncertainty bounding set, family, and value set) are briefly recalled, with the accent on the ellipsoidal polynomial families. Subsequently, the non-convex value sets of the illustrative ellipsoidal polynomial family with multilinear uncertainty structure are plotted and analyzed. It is shown that the boundaries of the value set need not to mapped only from the boundaries in the parameter space but possibly also from the internal points. © 2019, Springer Nature Switzerland AG.