Analysis of a Model Set in the Dual Chain-Scattering Representation Based on the Graph Topology

Abstract

We consider a model set in the dual chain-scattering framework. Given a rational transfer function matrix which we call a generator, a model set is defined by the dual Homographic transformation of the generator and the norm-bounded linear time-invariant uncertainty. We show that the continuity of the dual Homographic transformation with respect to the graph topology is necessary for robust stabilization of two class of controllers; LTI controller and NLTV controller. Moreover, for each class of controller, certain conditions must be included.