Model Reduction in the Presence of Uncertainty in Model Parameters

This short note describes how to extend a certain class of existing model reduction techniques to take into account uncertainty in model parameters. The key idea of this extension is that the reduced-order model should not only contain the model parameters, but that the reduction procedure itself has to be geared for dealing with parametric uncertainty. This goal is achieved by augmenting the vector of inputs to the system with the uncertain parameters and by performing model reduction on the augmented system. It is shown that error bounds for the reduced order model can be computed if the underlying system is linear with respect to the states, parameters, and inputs. A comparison between the presented technique and a conventional approach is made via two examples.