State-space μ -analysis for an experimental drive-by-wire vehicle

This paper considers the application of the skewed structured singular value to the robust stability of systems subject to strictly real parametric uncertainty. Three state-space formulations that counteract the discontinuous nature of this problem are detailed. It is shown that the calculation of the supremum of the structured singular value over a frequency range using these formulations transforms into a single skewed structured singular value calculation. Like the structured singular value, the calculation of the exact value of the skewed structured singular value is a NP-hard problem, therefore alternative, less computationally demanding algorithms to determine upper and lower bounds are necessary. Two algorithms that determine upper and lower bounds on the skewed structured single value are presented. These algorithms are critically assessed by performing a robust stability analysis on a safety-critical experimental drive-by-wire vehicle.