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. Similar to the structured singular value, the exact calculation of the skewed structured singular value is an NP-hard problem. In this work, two efficient algorithms that determine upper and lower bounds on the skewed structured singular value are presented. These algorithms are critically assessed using a series of robustness analysis tests on a safety-critical experimental drive-by-wire vehicle.