A robust-control-relevance perspective on model order selection

High-performance robust control hinges on explicit compensation of performance-limiting system phenomena. Hereto, such phenomena need to be described with high fidelity by the model set. Clearly, this demands for a delicate mutual selection of the nominal model and the uncertainty bound. Both should have a limited complexity to enable successful controller synthesis and implementation. The aim of this paper is to investigate model order selection for robust-control-relevant identification. Therefore, it is investigated how the worst-case performance that is associated with a model set is influenced by the complexity of the nominal model and the uncertainty bound. It turns out that, using a judiciously selected uncertainty coordinate frame, worst-case performance can be made invariant for the order of the uncertainty bound. Nevertheless, dynamic uncertainty modeling may still be worthwhile when accounting for approximations that are commonly made in robust-control-relevant identification, as is analyzed in this paper as well.