Identification of uncertain systems described by linear fractional transformations

We presents a framework for robust identification of uncertain LTI systems. Robust identification deals with the problem of finding models in a model class that best approximate the underlying uncertain system. Identification of uncertain systems arise whenever the underlying system cannot be adequately described by the model class chosen for the purpose of identification. A notion of robust consistency is introduced to deal with the problem of consistent estimation of the best model belonging to a predefined model class. We derive necessary and sufficient conditions for robust consistency, which establishes the optimality of well-known instrument-variable techniques for robust consistency. We show that these conditions amount to the existence of an instrument-input-pair capable of annihilating the residual error as well as stochastic noise. These concepts are then applied to establish robust consistency for several classes of uncertain systems described by linear fractional transformations.