Identification of the Smallest Unfalsified Model Set with both Parametric and Unstructured Uncertainty

Abstract In this paper, we consider a model set identification problem, in which we try to find a transfer function set such that the set can reproduce given input/output data in the time domain. The set is characterized by nominal parameters and two types of uncertainty, that is, the l-norm-bounded time-varying parametric and the H-norm-bounded time-invariant unstructured uncertainty. This identification problem is solved in two stages. First, we find a transfer function set with only parametric uncertainties by a geometric idea in a parameter space. The obtained model set is shown to be transformed into the LFT form, to which we can apply the available robust control theory. Second, we deal with both parametric and unstructured uncertainties by applying the Caratheodory-Fejer Extension Theorem to the transfer function set. It is shown that all the problems formulated in this paper can be reduced to convex optimization problems.