Linear Systems With Uncertain Complex Coefficients for AC Sensitivity Analysis

This paper deals with the characterization of the set of exact solutions to uncertain complex linear systems, with a particular focus on those encountered in the frequency analysis of electrical networks. We assume that the real and imaginary parts of the uncertain parameters belong to predefined intervals, and we aim to characterize the set of all possible solutions. Our main result shows that sensitivity analysis with respect to variations of a single element can be performed exactly, as the sets of exact solutions for all variables are bounded by circular arcs. When several elements of the network are simultaneously subject to variations, the solution sets can be characterized by adopting appropriate circle arcs to approximate their boundaries, with considerable precision.