Systems modeling, analysis and control (SMAC) toolbox: An insight into the robustness analysis library

The analysis library of the new SMAC Toolbox for Matlab implements a set of μ-analysis based tools to evaluate the robustness properties of linear time-invariant systems affected by time-invariant uncertainties. These tools allow to compute both lower and upper bounds on the (skewed) robust stability margin, the worst-case H_∞ performance level, as well as the worst-case 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.