This thesis considers time-domain model validation and approximation of models with parametric uncertainty from a closed-loop perspective. Two methods of time-domain model validation using noise corrupted input/output data are presented. The first algorithm uses frequency-wise analysis to identify the smallest H-infinity ball of single-input, single-output systems which are consistent with the data and a priori assumptions. The algorithm is polynomial time with respect to model order and can obtain arbitrary precision. The motivation for this set membership approach to validation is the fact that closed-loop stabilization can be assessed on a frequency-wise basis; therefore, the results of this algorithm provide a non-conservative test for assessing the robust stabilization of the set of all systems which could have produced the experimental data.

The second proposed validation algorithm provides sharper results than those of the first algorithm by working with the nu-gap metric. Experimental (in)validation of a discrete-time, multi-input, multi-output, nominal model is assessed by determining if observed input/output data is consistent with a system which is within a given nu-gap distance from the model. The general problem has been shown to be NP-hard; however, we present linear matrix inequality sufficient conditions for model consistency along with similar necessary and sufficient conditions for invalidation with respect to a special class of input/output noise. A logical extension which considers time-varying perturbations of the nominal model is presented in parallel with the time-invariant nu-gap results.

Finally, a novel method of approximation of a system with possibly non-linear dependence upon parametric uncertainty parameters is proposed. This method makes approximations of the system with respect to the nu-gap metric in order to generate an approximate model with linear fractional dependence upon the uncertainty parameters. Due to the close relationship between the nu-gap metric and H-infinity loop-shaping performance, this type of model approximation can be used to investigate the effect of the uncertainty parameters on closed-loop performance. This method can also identify uncertainty parameters which may be disregarded since they should have no significant effect on closed-loop performance. Results from the application of these approximation techniques to a benchmark model of a highly manoeuvrable aircraft are presented.

Keywords: model validation, parametric uncertainty, nu-gap metric, robust performance, control system analysis