Approximation of achievable robustness limit based on sensitivity inversion

Introduction: The sensitivity function, defined as the closed-loop transfer function from the exogenous input to the tracking error, is central to the multi-objective design and analysis of a feedback control system. Its frequency response determines many performance characteristics of the closed-loop system, such as disturbance attenuation, reference tracking, and robustness against uncertainties and noise. It is well known that the nominal sensitivity peak, i.e., the H∞ -norm of the sensitivity function, is a direct measure of stability robustness, because the sensitivity magnitude quantifies both the attenuation of the effect of external disturbances on the closed-loop output and the variations of the closed-loop system with respect to the plant perturbations