Derivation and selection of norm-bounded uncertainty descriptions based on multiple models

A method for determining a norm-bounded unstructured uncertainty description from a set of linear models is presented. The method yields multiple-input, multiple-output shaping filters which are suitable for H(infinity)-based analysis or controller synthesis. The method can be applied to so-called model matching, where uncertainty descriptions are obtained from a set of linear models. Another approach is to use so-called output matching, which utilises outputs of the models in the set. First, necessary and sufficient conditions for uncertainty shaping filters to capture a multimodel set are given. Then, an approach for non-conservative filter design by optimizing a closed-loop criterion is proposed. It is highlighted by a design example, where additive, input-multiplicative and output-multiplicative uncertainty models are compared. The example illustrates the impact of the choice of uncertainty model and the structure of the shaping filter on the resulting conservatism caused by the uncertainty description.