A search algorithm for the compact uncertainty region of system elements with interval and affine constraint properties

This study proposes a search algorithm for the compact uncertainty region of system elements with affine constraints and interval information. While existing studies have considered only the interval information of uncertainty, the proposed algorithm reflects both the interval and affine constraints of uncertain elements to reduce conservatism due to uncertainties. First, the affine constraints of uncertainty are plotted in an N-dimensional space, where N is the number of elements that should be considered. Due to the properties of the affine constraints, the affine constraints are expressed as an (N-1) dimensional structure. The interval information is then expressed as an N-dimensional structure. The algorithm iteratively checks the edges of the N-dimensional structure between two geometrical structures to determine the intersection region. The algorithm then collects the vertices of the convex polytope that overlap the two structures. To show the effectiveness of proposed algorithm, this study proposes a consensus criterion for a multi-agent time-delayed system with uncertain switching topologies as an application of a system with uncertainties in system elements.