Sensitivity-based link addition for robust linear dynamical networks

A link addition problem is considered for a directed linear network in order to improve the network robustness. The robustness of network is quantified through a well-known measure of stability margin. Optimal identification of links such that the stability margin is maximized by their addition, requires solving a complex combinatorial problem. Here two efficient methods are proposed for suboptimal link addition by exploiting the sensitivity being embedded in the derivative of singular value and Lagrange multiplier. Numerical tests are presented to demonstrate the efficacy of the proposed methods.