Generalized real perturbation values with applications to the structured real controllability radius of LTI systems

This paper generalizes the notion of real perturbation values of a complex matrix to account for a more general perturbation structure. Formulas for computing the so-called generalized real perturbation values of a matrix are derived and presented. Using these results, we revisit the computation of the structured real controllability radius that was previously used to evaluate the robustness of the multi-link inverted pendulum system, and we also study a new normalized version of the transmission zero at s radius.