Data-Based Modeling of Block-Diagonal Uncertainty by Convex Optimization

A procedure for deriving norm-bounded uncertainty models for MIMO systems is presented. Additive as well as multiplicative input and output uncertainty models with structured or unstructured uncertainty are treated in a unified manner. The main focus in this paper is on structured (block diagonal) uncertainty. 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 the size of an uncertainty region subject to necessary and sufficient data-matching conditions. The calculations, which are done frequency by frequency, are formulated as a convex optimization problem using LMIs as constraints. In an application to uncertainty modeling of a distillation column various structural types of uncertainty models are compared.