Sensitivity Mapping of Closed-Loop Root Contours from Robust Admissibility to Local Fragility

Robust admissibility guarantees that the closed-loop poles remain within a prescribed region, but it does not reveal the locally sensitive portions of the root contours. In this study, a pole sensitivity mapping method is developed that combines modulus–phase decomposition, multiparametric assessment using singular values, and time-domain verification. The method is applied to an uncertain second-order plant with a PI controller and seven tunings numerically confirmed as robustly admissible. For the considered tunings, the maximum local pole sensitivity varies from 1.388 to 43.951, with the tuning having the lowest pole sensitivity not coinciding with having the lowest transient response sensitivity. The results show that the joint quantitative consideration of pole and time-domain sensitivities enables a more substantiated selection among robustly admissible tunings by localizing fragile regions and identifying the nature of pole motion.