A set of μ-analysis based tools to evaluate the robustness properties of high-dimensional uncertain systems

This paper reviews a set of μ-analysis based tools developed by the authors during the last decade to evaluate the robustness properties of high-dimensional linear plants subject to numerous time-invariant uncertainties. These tools allow to compute both upper and lower bounds on the robust stability margin, the worst-case H
_∞
performance level, as well as the traditional gain, phase, modulus and time-delay margins. The key idea is to solve the problem on just a coarse frequency grid and to perform a fast validation on the whole frequency range, which results in guaranteed but conservative bounds on the aforementioned quantities. Some heuristics are then applied to determine a set of worst-case parametric configurations leading to over-optimistic bounds. A branch and bound scheme is finally implemented, so as to tighten these bounds with the desired accuracy, while still guaranteeing a reasonable computational complexity. The proposed algorithms are successfully assessed on a challenging real-world application.