Optimal Frequency-Domain Uncertainty Quantification for MIMO Systems Using Normalised Hausdorff Measure

Uncertainty quantification is essential for robust controller synthesis to ensure stability and performance under varying conditions, parameters, and external disturbances. To reduce the conservatism in the controller design, a 'tight' description of the uncertainty is crucial. While traditional frequency-domain methods provide effective uncertainty descriptions for single-input single-output (SISO) systems, they often yield inadequate and overly conservative representations in multi-input multi-output (MIMO) settings. This paper proposes a novel measure of the uncertainty that provides a better description of the uncertainty sets for MIMO systems. Additionally, it presents a computationally efficient method for optimising the frequency-domain uncertainty set while simultaneously determining the nominal model. The method also considers the case where set-bounded noise and modelling errors are present and known. The proposed method's effectiveness is validated using comparisons with the traditional methods. Finally, high-performance robust controllers are synthesised and implemented for uncertainty sets obtained using different uncertainty quantification methods on a hybrid micro-vibration rejection platform, demonstrating improved performance and reduced conservatism for the proposed method.