Derivation of Unstructured MIMO Uncertainty Models via Data Matching

A procedure for deriving norm-bounded uncertainty models for MIMO systems is presented. Additive as well as multiplicative input and output uncertainty models with unstructured uncertainty are treated in a unified manner. The models are determined by matching the input-output behavior of an uncertainty model to sets of input-output data obtained, e.g., through system identification. Tight bounds are achieved by minimization of an ellipsoidal uncertainty region subject to a data-matching condition, which is both necessary and sufficient to guarantee an uncertainty model that is compatible with the known input-output data. Uncertainty weights can be calculated frequency by frequency but uncertainty filter transfer functions can also be fitted directly. The important task of choosing the correct type of uncertainty description is also addressed.