Model validation for nonlinear feedback systems

Model validation provides a useful means of assessing the ability of a model to account for a specific experimental observation, and has application to modeling, identification and fault detection. In a robust control framework norm-bounded perturbations are included to account for dynamic uncertainties in the system. We consider a discrete-time or sampled-data framework with a general linear fractional transformation (LFT) model structure which allows for the consideration of nonlinear feedback structures. Block structured, causal time-varying perturbations are considered and we give a sufficient condition-necessary and sufficient in the single perturbation block case-for the model to be invalidated by the datum. The condition is testable by a convex LMI feasibility problem in which the matrix basis grows linearly in size with respect to the data length and the number of decision variables is equal to the number of perturbation blocks.